Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 248537 8 pageshttpdxdoiorg1011552013248537

Research ArticleThe Impact of the Subsidy Policy on Total Factor ProductivityAn Empirical Analysis of Chinarsquos Cotton Production

Yanwen Tan1 Jianbo Guan1 and Hamid Reza Karimi2

1 College of Economics and Management South China Agricultural University Guangzhou Guangdong 510642 China2Department of Engineering Faculty of Engineering and Science University of Agder 4898 Grimstad Norway

Correspondence should be addressed to Hamid Reza Karimi hamidrkarimiuiano

Received 7 December 2012 Accepted 12 January 2013

Academic Editor Xiaohang Yue

Copyright copy 2013 Yanwen Tan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper develops one model to explore the relationship between the subsidy policy and the agricultural total factor productivity(TFP) It indicates that the agricultural TFP will be lower after the subsidy policy is implemented and there exists a negative relationbetween the subsidy and TFP if subsidies are associated with the acreage Using Malmquist index this paper measures the changesof TFP in Chinarsquos cotton production before and after the subsidy policy is implemented The results verify that the subsidy policycould not increase but decrease the TFP of Chinarsquos cotton production not only in the whole country but also in major provinces ofChina Based on the positive study some policy implications are provided in the end of this paper

1 Introduction

11 Background China is the largest country in producingand consuming cotton in the world From 2000 to 2010Chinarsquos average annual output of cotton reached 68 mil-lion metric tons which accounts for almost 30 of globalaverage annual cotton output (Chinese data are from ldquoChinaStatistical Yearbookrdquo National Bureau of Statistics of Chinaworld data are from ldquoCotton and Wool Yearbookrdquo USDA)After accessing to WTO China has become gradually thelargest importer of cotton From2002 to 2011 China importedcotton accumulated to 2110 million metric tons (Figure 1)with average annual import of 213millionmetric tons whichaccounts for 273of the quantity of global cotton import (theaverage annual trading quantity of world cotton from 2002 to2011 is 78 million metric tons according to the statistics ofldquoCotton and Wool Yearbookrdquo USDA)

From 2002 to 2006 in the first 5 years after becomingWTO member China imported more and more cotton(Figure 2) with the average annual growth rate of 1448especially in 2006 China imported 364 million metric tonswhich was 19 folds than that in 2002 The reason that Chinaimported so much quantity of cotton is because of the huge

increase of Chinarsquos export of textile after accessing WTOand in particular cancellation of ldquoMultifibre Arrangement(MFA)rdquo In 2005 China exported a total $11503 billion oftextiles and garments representing a 21 increase over theprevious year in 2006 Chinarsquos exported textiles and garmentsreached $14397 billion an increase of 25 over the year of2005 But at the same time Chinarsquos cotton production had notbeen increased much enough (Figure 3) In order to motivatethe farmers to produce more cotton to meet the constantlyincreasing requirement of cotton Chinarsquos government carriedout one subsidy policy on cotton seed in high quality(simplified as ldquoseed subsidyrdquo in the following contents) insome areas in 2007 with 15 yuan RMB per mu (mu is a unitof measuring area in China one hectare equal to 15 mus)and then fully implemented the subsidy policy in all cottonproducing areas from 2009 The aim of the seed subsidy is toencourage farmers to buy the cotton seed in high quality soas to increase the output and the productivity However from2008 Chinarsquos cotton output showed consecutive reduction inthree years It apparently means that the seed subsidy policyhas not gotten the devising aim to increase the productivityand the output of cotton How to interpret this phenomenonIs there any rule behind this phenomenon This paper will

2 Mathematical Problems in Engineering

003 079 269

525

888 1132

1341 1494

1777

211

0

5

10

15

20

25

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Figure 1 Chinarsquos net accumulated import cotton from 2002 to2011 Unit million MTs Data source ldquoChina Statistical YearbookrdquoNational Bureau of Statistics of China

005 006 018

087

191

257

364

246 211

153

284

336

0

05

1

15

2

25

3

35

4

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Figure 2 The import cotton of China from 2000 to 2011 Unitmillion MTs Data source ldquoChina Statistical Yearbookrdquo NationalBureau of Statistics of China

0200400600800100012001400

0100020003000400050006000700080009000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Area (1000 He)Output (1000 Mt)Yield (KgHe)

Figure 3 The situation of Chinarsquos cotton production from 2000 to2010 Data source ldquoChina Statistical Yearbookrdquo National Bureau ofStatistics of China

investigate the relationship between the subsidy policy andthe productivity using a theoretical model and will positivelyanalyze the impact of the subsidy policy on the total factorsproductivity (TFP) of Chinarsquos cotton production

12 The Literature Review Regarding the relationship be-tween the subsidy policy and agricultural productivity there

are many empirical studies concluded one negative rela-tionship existed between them Giannakas et al [1] foundusing the data of farms in the Province of SaskatchewanCanada that subsidies had a negative effect on technicalefficiency during the period of 1987 to 1995 Rezitis etal [2] indicated that subsidies granted to Greek farmershad a negative impact on Greek farmsrsquo technical efficiencyGuyomard et al [3] investigated the subsidies productivitychanges of crop beef meat and dairy farms in French overthe period of 1995 to 2002 using Malmquist Indices andthey indicated that the subsidies had a negatively influenceon the technical efficiency scores but positively change inboth technical efficiency and productivity Sabir and Ahmed[4] used variance decomposition approach to estimate theimpact of economic reforms on TFP growth for the overalleconomy of Pakistan using time series data from 1972-1973 to 2001-2002 They included index of human capitalfertilizer subsidy food subsidy as the independent variablesand index of TFP as the dependent variable Their resultsshowed that the impact of food subsidy was negligible withan elasticity coefficient of only 0003 fertilizer subsidy hada negligible negative impact on TFP Nivievskyi [5] analyzedthe productivity growth in Ukrainian dairy farming andindicated the price supports that negatively impacted theefficiency Latruffe et al [6] applied a five-step approach tothe investigation of the relationship between public subsidiesnamely CAP (common agricultural policy) direct paymentsand managerial efficiency for French CAP and beef farmsin 2000 The conclusion showed that there was a strong sig-nificant negative relationship between managerial efficiencyand CAP direct payments Mary [7] analyzed the impact ofCAP subsidies on total factor productivity of French cropfarms between 1996 and 2003 and the results also showedthat several subsidies have a negative impact on productivityBut Kazukauskas and Newman [8] found that the decouplingpolicy had positive significant effect on the farm productivityAnd Rizov et al [9] found that subsidies impacted negativelythe farm productivity in the period before the decouplingreform was implemented after decoupling the effect ofsubsidies on productivity was more nuanced as in severalcountries it turned positive

As for Chinarsquos agricultural subsidy policy most Chineseliteratures focus on grain production and there are twodifferent viewpoints in the literatures The positive viewpointconsiders that the subsidy policy increases the farmersincome [10] and substantially enlarges the production ofgrain [11] Subsidies for agricultural machinery and seedpromote the production of grain [12] especially the subsidiesfor purchasing agricultural machinery significantly impactincreasing revenue of farmers in large scale who use lotsmachines to plant and harvest [13] However the negativeviewpoint thinks that subsidies do not have any influenceon farmers to enlarge the investment on agriculture becausethere is not any causality between subsidies and the farmerrsquosinvestment [14] since the subsidies could not offset thenegative impact from increasing producing cost so subsi-dies do not have enough incentive function for farmers toenhance their willingness to produce more grain [15 16]Less literatures concern Chinarsquos cotton subsidy According

Mathematical Problems in Engineering 3

to the multiobjective optimization model with discrete dataproposed in the references [17ndash22] Ding et al [17] establisheda model of multiobjective linear optimization and simulatedwhich subsidy could promote cotton production using thedata before 2007 and without subsidy in that period Theyconcluded that China should carry out multisubsidy insteadof seed subsidy such as subsidies for irrigation andmachines

Till now no literature explores the relationship betweensubsidy policy and productivity in theory and no literaturehas positively studied the relationship between subsidy policyand Chinarsquos cotton productivity This paper develops onemathematical model which theoretically demonstrates therule between the subsidies-related acreage and agriculturalTFP In order to verify the implication of the model thispaper will compare the TFP of Chinarsquos cotton productionbefore and after implementing the subsidy policy throughmeasuring Malmquist index The structure of this paper is asfollows Section 2 will derive and discuss one mathematicalmodelwhich investigates the theoretical relationship betweenthe seed subsidy and productivity Section 3 will make anempirical study of subsidy on Chinarsquos cotton TFP based onMalmquist index at last the paper will give the conclusionand some policy implications

2 A Theoretical Model

In order to observe what happened in Chinarsquos cotton produc-tivity after implementing seed subsidy we hereby establishtwo different profit functions

At first we consider the situation without subsidy Sup-posing farmerrsquos decision of planting cotton is based on priceso the planting area of cotton which reflects the producingdecision of farmers is a function of price

119878119897 = 119886 + 119887119901 (1)

119878119897 denotes the farmerrsquos planting area 119886 is a constant thatdenotes the initial planting area and 119901 denotes the price ofcotton The parameter 119887 is a marginal effect which reflects aunit change of 119878119897 upon119901 changing one unit and 119887 is a positivenumber which means that farmers will enlarge the plantingarea along with the price increasing

Suppose that yield is a Cobb-Douglas production func-tion in order to simplify the question we assume that laboris only one factor of input

119910 = 119864119897120572 (2)

Formula (2) describes the yield per unit planting area inwhich 119910 denotes the yield 119897 is the labor 120572 is the elasticity oflabor and 119864 is the labor efficiency which denotes the totalfactor productivity (TFP) in a certain So we get the profitfunction as follows

120587 = 119901119910119878119897 minus 1198620119878119897 (3)

In formula (3) 120587 denotes the profit and 1198620 denotes theproducing cost per mu Substitute 119878119897 and 119910 with formulas (1)and (2) respectively we can get the profit function as follows

120587 = 119901119864119897120572(119886 + 119887119901) minus 1198620 (119886 + 119887119901) (4)

Maximizing 120587 using first-order condition of function (3)with respect to 119901 equal to zero we can get the TFP function

119864 =1198620119887

(119886 + 2119887119901) 119897120572 (5)

Second we consider the farmerrsquos decision of producingunder the subsidy policy Chinarsquos cotton seed subsidy is 15Yuan per mu This kind of policy means the more area ofplanting cotton the more subsidies getting from governmentSo apparently Chinarsquos government wishes to increase thecotton production through stimulating farmers to enlargetheir cotton planting area using subsidy Then the plantingarea is certainly a function of subsidy

119878119897 = 119886 + 119887119901 + 119888119878119887 (6)

119878119887 denotes the subsidy and the parameter of 119888 is positive thatmeanswhen the subsidy paid to the farmers the planting areawill be increased which conforms the governmentrsquos wish

So we get another profit function as follows

120587 = 119901119910119878119897 + 119878119887119878119897 minus 1198620119878119897 (7)

Define 119910 = 119864119904119897120572 in formula (7) so Maximizing 120587 using

first-order condition of function (7) with respect to 119901 equalto zero and substituting 119878119897 with formula (6) we can get the119864119904 (the TFP after subsidy is carried out) as follows

119864119904 =1198620119887

(119886 + 2119887119901) 119897120572minus

(119887 + 119888) 119878119887

(119886 + 2119887119901) 119897120572 (8)

Apparently 119864119904 lt 119864 because (119887 + 119888)119878119887(119886 + 2119887119901)119897120572gt 0

So the TFP will be lower after the subsidy and there is anegative relationship between the TFP and the subsidy Theabove theoretical model reveals that the agricultural TFP willdecline when subsidy is implemented if the subsidy is relatedto planting area

3 Measuring Chinarsquos Cotton TFP

31 Model and Data Since the late 1990s Malmquist indexbased on Data Envelopment Analysis (DEA) method hasbeen widely used to measure and decompose the TFP andit is convenient to apply DEA techniques to capture the effectof the technical inefficiency [18] Malmquist index was putforward in 1953 by Malmquist [19] the Swedish economistand statistician and then Caves et al [20] and Fare et al [21]developed Malmquist index to measure TFP

311 Definition and Decomposition of the Malmquist IndexMalmquist index is a ratio of distance function in differentperiods The distance function is a technical one with multi-input andmultioutput without any assumptions in producerrsquosbehavior

Assuming that 119883 is a 119881-dimensional vector of inputfactors 119884 is 119882-dimensional vector of output and 119874(119883)denotes the set of output which is bounded closed and

4 Mathematical Problems in Engineering

convex According to Shepherd [22] the output distancefunction119863119900(119883 119884) on the bases of 119874(119883) is as follows

119863119900 (119883 119884) = Min120601 (119884120601) isin 119874 (119883) (9)

Let (119883119905119900 119884119905

119900) and (119883119905+119894

119900 119884119905+119894

119900) denote the input and output

vectors respectively in period 119905 and 119905 + 119894 119863119905119900(119883119905

119900 119884119905

119900) is the

output distance function based on the technology in period119905 119863119905119900(119883119905+119894

119900 119884119905+119894

119900) is the output distance function in 119905 + 119894 with

the technology in 119905If the technology changed from period 119905 to 119905 + 119894 the

Malmquist index in respect of output in period of 119905 is asfollows

119872119905

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900) (10)

Similarly the Malmquist index on the respect of outputin period 119905 + 119894 is as follows

119872119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900) (11)

Fare et al [21] adopted geometric mean of Malmquistindex in two periods as the definition in order to avoid errorsexisted in different periods which are selected random

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

(12)

Malmquist index could be decomposed as follows

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

=

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)

times [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905+119894119900 119884119905+119894119900)times119863119905

119900(119883119905

119900 119884119905

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

= Ech119900 times Tch119900(13)

where Ech119900 and Tch119900 denote the efficiency change and thetechnical change from period 119905 to period 119905 + 119894 respectively

Usually Malmquist Index could be gotten by DEAmethod DEA is the nonparametric mathematical program-ming approach to frontier estimation Assume that there aredata on 119870 inputs and 119872 outputs on each of 119873 decisionmaking units (DMUs) The 119870 times 119873 input matrix 119883 and

the 119872 times 119873 output matrix 119884 represent the data of all 119873DMUs The purpose of DEA is to construct a nonparametricenvelopment frontier over the data points such that allobserved points lie on or below the production frontierFor each DMU we would like to obtain a measure of theratio of all outputs over all inputs such as where 119906 is an119872 times 1 vector of output weights and V is a 119870 times 1 vectorof input weights To select optimal weights we specify themathematical programming problem

Max119906V

(1199061015840119910119894

V1015840119909119894)

st

1199061015840119910119895

V1015840119909119895le 1 119895 = 1 2 119873

119906 V ge 0

(14)

In order to avoid an infinite number of solutions impos-ing V1015840119909119895 = 1 and using the duality in linear programming

we can derive an equivalent envelopment form as follows

Min120579120582

120579

st

minus119910119894 + 119884120582 ge 0

120579119909119894 minus 119883120582 ge 0

120582 ge 0

(15)

where 120579 is a scalar standing for the efficiency score for the119894th DMU It will satisfy 120579 le 1 with a value of 1 indicating apoint on the frontier and hence a technically efficient DMUSo calculating Malmquist Index in any adjacent two years(119894 = 0 1) equal to solving the DEA model of the followingfour distance functions

[119863119905

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905+1

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905+1

119900

120579119895 ge 0 119895 = 1 2 119873

Mathematical Problems in Engineering 5

[119863119905

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

119873

sum

119895=1

120579119895 = 1 120579119895 ge 0 119895 = 1 2 119873

(16)

In the above models 119883 denotes input vectors 119884 denotesoutput vectors 120601 (0 lt 120601 lt 1) is a scalar which denotes theefficiency of technology of 119895 decision-making unit under thecondition of constant return to scale and 119895 = 1 2 119873 120579119895is a constant vector

312 Data Description The importance of nonparametricMalmquist index analysis is that the selected variables shouldreflect the input and output of cotton production perfectlyWe will use the labor values (standard working day) directmaterial costs and overhead expenses per mu as the inputfactors and cotton yield per mu as the output In order to getthe accurate conclusion we will measure the TFP of Chinarsquoscotton production not only for the whole country but alsofor every major producing cotton province So we choosethe input-output data of the whole nation and provincesof Hebei Shandong Anhui Jiangxi Hubei Hunan andXinjiang which are the main areas to plant cotton in ChinaAll the data are available from ldquoChina Statistics Yearbookrdquowhich is published by National Bureau of Statistics of Chinaand from ldquoAgricultural Costs and Benefitsrdquo which is editedby Chinarsquos National Development and Reform CommissionThe Malmquist index is solved and decomposed by softwareDEAP 21

32 Positive Results Figure 4 presents the results of Malm-quist index of Chinarsquos cotton production from 2001 to 2010Before the implementation of subsidy policy from 2001 to2006 the average annual growth rate of Malmquist indexwas 26 The Malmquist indices increased in most of yearsespecially increased up to 156 and 108 in 2001 and2006 than in 2000 and 2005 respectively At the same timeaccording to the decomposition results of Malmquist indexthe average annual value of technological change (Techch)increased by 47 (see Figure 5)

However after the implementation of the cotton seedsubsidy policy from 2007 the average annual values of

1156 107

0809

1076

0939

1108

0944 0918

1029 091

0

02

04

06

08

1

12

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 4 Chinarsquos cotton production Malmquist index

1257

1089

089

1081

0896

1068 1017 0921 0902 0849

0

02

04

06

08

1

12

14

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 5 Chinarsquos cotton production technological change

national Malmquist index decreased by 50 from 2007 to2010 Particularly in 2010 the decrease rate was up to 90The average annual changing rate of Techch was minus78 from2007 to 2010

In order to further test the change of cotton productivitywe continue calculating theMalmquist index and the techno-logical change of major provinces in China Figures 6 and 7report that all the provinces we selected were in the situationof declining Malmquist indices after the implementation ofseed subsidy (the details are shown in Table 1) From 2007to 2010 the average annual changing rates of Techch in theprovinces ofHebei Shandong Anhui Jiangxi Hubei Hunanand Xinjiang decreased 38 72 98 84 63 108and 21 respectively and the Malmquist indices decreased32 66 86 86 83 68 and 21 respectively

4 Conclusion and Policy Implications

41 Conclusion Subsidy is an important policy carried onthe agricultural department in many countries especiallyin developed countries However most literatures foundthat the subsidy could reduce instead of increasing theagricultural TFP There is the same phenomenon that existedin Chinarsquos cotton industry The output of Chinarsquos cotton hadbeen decreasing from 2008 to 2010 after implementing seedsubsidy policy in 2007This paper develops onemathematicalmodel to theoretically interpret what would happen about

6 Mathematical Problems in Engineering

Table 1 Chinarsquos cotton Malmquist index and technical change

Year 2001 2002 2003 2004 2005 2006 2001ndash2006 average 2007 2008 2009 2010 2007ndash2010 average

Country Malmquist index 1156 107 0809 1076 0939 1108 1026 0944 0918 1029 091 095Techch 1257 1089 089 1081 0896 1068 1047 1017 0921 0902 0849 0922

Hebei Malmquist index 0975 094 0899 0987 0911 1341 1009 1088 0931 0954 0898 0968Techch 0975 1133 0877 1077 0938 111 1018 1146 1025 0856 082 0962

ShandongMalmquist index 1055 0919 0902 0893 0987 1307 1011 0936 1001 0962 0835 0934Techch 1151 1108 0895 1066 0876 1115 1035 1065 0918 0897 0831 0928

Anhui Malmquist index 1354 1083 055 1201 077 1192 1025 1004 0712 1045 0896 0914Techch 1291 1083 0809 1047 0828 1077 1023 0923 0942 0909 0852 0907

Jiangxi Malmquist index 117 1097 0833 0967 1111 113 1051 0848 0883 1053 087 0914Techch 1513 1007 0754 1188 0814 1072 1058 0973 093 0938 0822 0916

Hubei Malmquist index 1678 1196 0868 0946 1135 1149 1162 0925 0978 0935 0831 0917Techch 1493 1142 0835 1239 0828 1149 1114 0925 1015 098 0826 0937

Hunan Malmquist index 1669 1306 0865 0848 0751 1275 1119 0802 0787 136 0777 0932Techch 125 1072 0865 1014 0826 1071 1016 0923 0903 0932 0808 0892

Xinjiang Malmquist index 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979Techch 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979

002040608

11214

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 6 Cotton Malmquist indices in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

the TFP after the subsidy policy was implemented Themodel indicates that TFP would be lower after the subsidywas implemented and there exists a negative relationshipbetween the subsidy policy andTFP if the subsidy is related toplanting area Using the input-output data of Chinarsquos cottonproduction this paper calculates theMalmquist index whichis the representative of the TFP and the technology progressof the whole country and major provinces from 2001 to 2010The conclusion is that the TFP of Chinarsquos cotton productiondecreased after seed subsidy was implemented from 2007not only in the whole country but also in major provincesin China So the seed subsidy policy has failed to effectivelyincrease the TFP of Chinarsquos cotton production

42 Policy Implications Thepositive conclusion of this papercould give us many important policy implications Firstlythe subsidy policy could not increase the agricultural TFP

0

02

04

06

08

1

12

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 7 Cotton technological changes in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

providing the subsidy related to the acreage Chinarsquos cottonseed subsidy is given to farmers according to their plantingarea the only one effect of the seed subsidy is to encouragefarmers to add acreage instead of adding other inputs andof course enlarging area is no means of increasing TFP Onthe contrary subsidy policy would breed inertia to farmersbecause farmers could get the subsidy from governmentas long as they plant cotton regardless how much yieldthey would harvest Secondly subsidy could be regarded asone kind of income which has the feature of stickiness aswage So the quantity of subsidy paid to farmers shouldbe increased constantly otherwise farmers would not besatisfied with the government From the above mentionedtwo aspects we could understand why there is a negativerelationship between the subsidy which is related to plantingarea and the productivity because the subsidy could notmotivate farmers to produce zealously and efficiently

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

003 079 269

525

888 1132

1341 1494

1777

211

0

5

10

15

20

25

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Figure 1 Chinarsquos net accumulated import cotton from 2002 to2011 Unit million MTs Data source ldquoChina Statistical YearbookrdquoNational Bureau of Statistics of China

005 006 018

087

191

257

364

246 211

153

284

336

0

05

1

15

2

25

3

35

4

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Figure 2 The import cotton of China from 2000 to 2011 Unitmillion MTs Data source ldquoChina Statistical Yearbookrdquo NationalBureau of Statistics of China

0200400600800100012001400

0100020003000400050006000700080009000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Area (1000 He)Output (1000 Mt)Yield (KgHe)

Figure 3 The situation of Chinarsquos cotton production from 2000 to2010 Data source ldquoChina Statistical Yearbookrdquo National Bureau ofStatistics of China

investigate the relationship between the subsidy policy andthe productivity using a theoretical model and will positivelyanalyze the impact of the subsidy policy on the total factorsproductivity (TFP) of Chinarsquos cotton production

12 The Literature Review Regarding the relationship be-tween the subsidy policy and agricultural productivity there

are many empirical studies concluded one negative rela-tionship existed between them Giannakas et al [1] foundusing the data of farms in the Province of SaskatchewanCanada that subsidies had a negative effect on technicalefficiency during the period of 1987 to 1995 Rezitis etal [2] indicated that subsidies granted to Greek farmershad a negative impact on Greek farmsrsquo technical efficiencyGuyomard et al [3] investigated the subsidies productivitychanges of crop beef meat and dairy farms in French overthe period of 1995 to 2002 using Malmquist Indices andthey indicated that the subsidies had a negatively influenceon the technical efficiency scores but positively change inboth technical efficiency and productivity Sabir and Ahmed[4] used variance decomposition approach to estimate theimpact of economic reforms on TFP growth for the overalleconomy of Pakistan using time series data from 1972-1973 to 2001-2002 They included index of human capitalfertilizer subsidy food subsidy as the independent variablesand index of TFP as the dependent variable Their resultsshowed that the impact of food subsidy was negligible withan elasticity coefficient of only 0003 fertilizer subsidy hada negligible negative impact on TFP Nivievskyi [5] analyzedthe productivity growth in Ukrainian dairy farming andindicated the price supports that negatively impacted theefficiency Latruffe et al [6] applied a five-step approach tothe investigation of the relationship between public subsidiesnamely CAP (common agricultural policy) direct paymentsand managerial efficiency for French CAP and beef farmsin 2000 The conclusion showed that there was a strong sig-nificant negative relationship between managerial efficiencyand CAP direct payments Mary [7] analyzed the impact ofCAP subsidies on total factor productivity of French cropfarms between 1996 and 2003 and the results also showedthat several subsidies have a negative impact on productivityBut Kazukauskas and Newman [8] found that the decouplingpolicy had positive significant effect on the farm productivityAnd Rizov et al [9] found that subsidies impacted negativelythe farm productivity in the period before the decouplingreform was implemented after decoupling the effect ofsubsidies on productivity was more nuanced as in severalcountries it turned positive

As for Chinarsquos agricultural subsidy policy most Chineseliteratures focus on grain production and there are twodifferent viewpoints in the literatures The positive viewpointconsiders that the subsidy policy increases the farmersincome [10] and substantially enlarges the production ofgrain [11] Subsidies for agricultural machinery and seedpromote the production of grain [12] especially the subsidiesfor purchasing agricultural machinery significantly impactincreasing revenue of farmers in large scale who use lotsmachines to plant and harvest [13] However the negativeviewpoint thinks that subsidies do not have any influenceon farmers to enlarge the investment on agriculture becausethere is not any causality between subsidies and the farmerrsquosinvestment [14] since the subsidies could not offset thenegative impact from increasing producing cost so subsi-dies do not have enough incentive function for farmers toenhance their willingness to produce more grain [15 16]Less literatures concern Chinarsquos cotton subsidy According

Mathematical Problems in Engineering 3

to the multiobjective optimization model with discrete dataproposed in the references [17ndash22] Ding et al [17] establisheda model of multiobjective linear optimization and simulatedwhich subsidy could promote cotton production using thedata before 2007 and without subsidy in that period Theyconcluded that China should carry out multisubsidy insteadof seed subsidy such as subsidies for irrigation andmachines

Till now no literature explores the relationship betweensubsidy policy and productivity in theory and no literaturehas positively studied the relationship between subsidy policyand Chinarsquos cotton productivity This paper develops onemathematical model which theoretically demonstrates therule between the subsidies-related acreage and agriculturalTFP In order to verify the implication of the model thispaper will compare the TFP of Chinarsquos cotton productionbefore and after implementing the subsidy policy throughmeasuring Malmquist index The structure of this paper is asfollows Section 2 will derive and discuss one mathematicalmodelwhich investigates the theoretical relationship betweenthe seed subsidy and productivity Section 3 will make anempirical study of subsidy on Chinarsquos cotton TFP based onMalmquist index at last the paper will give the conclusionand some policy implications

2 A Theoretical Model

In order to observe what happened in Chinarsquos cotton produc-tivity after implementing seed subsidy we hereby establishtwo different profit functions

At first we consider the situation without subsidy Sup-posing farmerrsquos decision of planting cotton is based on priceso the planting area of cotton which reflects the producingdecision of farmers is a function of price

119878119897 = 119886 + 119887119901 (1)

119878119897 denotes the farmerrsquos planting area 119886 is a constant thatdenotes the initial planting area and 119901 denotes the price ofcotton The parameter 119887 is a marginal effect which reflects aunit change of 119878119897 upon119901 changing one unit and 119887 is a positivenumber which means that farmers will enlarge the plantingarea along with the price increasing

Suppose that yield is a Cobb-Douglas production func-tion in order to simplify the question we assume that laboris only one factor of input

119910 = 119864119897120572 (2)

Formula (2) describes the yield per unit planting area inwhich 119910 denotes the yield 119897 is the labor 120572 is the elasticity oflabor and 119864 is the labor efficiency which denotes the totalfactor productivity (TFP) in a certain So we get the profitfunction as follows

120587 = 119901119910119878119897 minus 1198620119878119897 (3)

In formula (3) 120587 denotes the profit and 1198620 denotes theproducing cost per mu Substitute 119878119897 and 119910 with formulas (1)and (2) respectively we can get the profit function as follows

120587 = 119901119864119897120572(119886 + 119887119901) minus 1198620 (119886 + 119887119901) (4)

Maximizing 120587 using first-order condition of function (3)with respect to 119901 equal to zero we can get the TFP function

119864 =1198620119887

(119886 + 2119887119901) 119897120572 (5)

Second we consider the farmerrsquos decision of producingunder the subsidy policy Chinarsquos cotton seed subsidy is 15Yuan per mu This kind of policy means the more area ofplanting cotton the more subsidies getting from governmentSo apparently Chinarsquos government wishes to increase thecotton production through stimulating farmers to enlargetheir cotton planting area using subsidy Then the plantingarea is certainly a function of subsidy

119878119897 = 119886 + 119887119901 + 119888119878119887 (6)

119878119887 denotes the subsidy and the parameter of 119888 is positive thatmeanswhen the subsidy paid to the farmers the planting areawill be increased which conforms the governmentrsquos wish

So we get another profit function as follows

120587 = 119901119910119878119897 + 119878119887119878119897 minus 1198620119878119897 (7)

Define 119910 = 119864119904119897120572 in formula (7) so Maximizing 120587 using

first-order condition of function (7) with respect to 119901 equalto zero and substituting 119878119897 with formula (6) we can get the119864119904 (the TFP after subsidy is carried out) as follows

119864119904 =1198620119887

(119886 + 2119887119901) 119897120572minus

(119887 + 119888) 119878119887

(119886 + 2119887119901) 119897120572 (8)

Apparently 119864119904 lt 119864 because (119887 + 119888)119878119887(119886 + 2119887119901)119897120572gt 0

So the TFP will be lower after the subsidy and there is anegative relationship between the TFP and the subsidy Theabove theoretical model reveals that the agricultural TFP willdecline when subsidy is implemented if the subsidy is relatedto planting area

3 Measuring Chinarsquos Cotton TFP

31 Model and Data Since the late 1990s Malmquist indexbased on Data Envelopment Analysis (DEA) method hasbeen widely used to measure and decompose the TFP andit is convenient to apply DEA techniques to capture the effectof the technical inefficiency [18] Malmquist index was putforward in 1953 by Malmquist [19] the Swedish economistand statistician and then Caves et al [20] and Fare et al [21]developed Malmquist index to measure TFP

311 Definition and Decomposition of the Malmquist IndexMalmquist index is a ratio of distance function in differentperiods The distance function is a technical one with multi-input andmultioutput without any assumptions in producerrsquosbehavior

Assuming that 119883 is a 119881-dimensional vector of inputfactors 119884 is 119882-dimensional vector of output and 119874(119883)denotes the set of output which is bounded closed and

4 Mathematical Problems in Engineering

convex According to Shepherd [22] the output distancefunction119863119900(119883 119884) on the bases of 119874(119883) is as follows

119863119900 (119883 119884) = Min120601 (119884120601) isin 119874 (119883) (9)

Let (119883119905119900 119884119905

119900) and (119883119905+119894

119900 119884119905+119894

119900) denote the input and output

vectors respectively in period 119905 and 119905 + 119894 119863119905119900(119883119905

119900 119884119905

119900) is the

output distance function based on the technology in period119905 119863119905119900(119883119905+119894

119900 119884119905+119894

119900) is the output distance function in 119905 + 119894 with

the technology in 119905If the technology changed from period 119905 to 119905 + 119894 the

Malmquist index in respect of output in period of 119905 is asfollows

119872119905

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900) (10)

Similarly the Malmquist index on the respect of outputin period 119905 + 119894 is as follows

119872119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900) (11)

Fare et al [21] adopted geometric mean of Malmquistindex in two periods as the definition in order to avoid errorsexisted in different periods which are selected random

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

(12)

Malmquist index could be decomposed as follows

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

=

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)

times [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905+119894119900 119884119905+119894119900)times119863119905

119900(119883119905

119900 119884119905

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

= Ech119900 times Tch119900(13)

where Ech119900 and Tch119900 denote the efficiency change and thetechnical change from period 119905 to period 119905 + 119894 respectively

Usually Malmquist Index could be gotten by DEAmethod DEA is the nonparametric mathematical program-ming approach to frontier estimation Assume that there aredata on 119870 inputs and 119872 outputs on each of 119873 decisionmaking units (DMUs) The 119870 times 119873 input matrix 119883 and

the 119872 times 119873 output matrix 119884 represent the data of all 119873DMUs The purpose of DEA is to construct a nonparametricenvelopment frontier over the data points such that allobserved points lie on or below the production frontierFor each DMU we would like to obtain a measure of theratio of all outputs over all inputs such as where 119906 is an119872 times 1 vector of output weights and V is a 119870 times 1 vectorof input weights To select optimal weights we specify themathematical programming problem

Max119906V

(1199061015840119910119894

V1015840119909119894)

st

1199061015840119910119895

V1015840119909119895le 1 119895 = 1 2 119873

119906 V ge 0

(14)

In order to avoid an infinite number of solutions impos-ing V1015840119909119895 = 1 and using the duality in linear programming

we can derive an equivalent envelopment form as follows

Min120579120582

120579

st

minus119910119894 + 119884120582 ge 0

120579119909119894 minus 119883120582 ge 0

120582 ge 0

(15)

where 120579 is a scalar standing for the efficiency score for the119894th DMU It will satisfy 120579 le 1 with a value of 1 indicating apoint on the frontier and hence a technically efficient DMUSo calculating Malmquist Index in any adjacent two years(119894 = 0 1) equal to solving the DEA model of the followingfour distance functions

[119863119905

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905+1

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905+1

119900

120579119895 ge 0 119895 = 1 2 119873

Mathematical Problems in Engineering 5

[119863119905

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

119873

sum

119895=1

120579119895 = 1 120579119895 ge 0 119895 = 1 2 119873

(16)

In the above models 119883 denotes input vectors 119884 denotesoutput vectors 120601 (0 lt 120601 lt 1) is a scalar which denotes theefficiency of technology of 119895 decision-making unit under thecondition of constant return to scale and 119895 = 1 2 119873 120579119895is a constant vector

312 Data Description The importance of nonparametricMalmquist index analysis is that the selected variables shouldreflect the input and output of cotton production perfectlyWe will use the labor values (standard working day) directmaterial costs and overhead expenses per mu as the inputfactors and cotton yield per mu as the output In order to getthe accurate conclusion we will measure the TFP of Chinarsquoscotton production not only for the whole country but alsofor every major producing cotton province So we choosethe input-output data of the whole nation and provincesof Hebei Shandong Anhui Jiangxi Hubei Hunan andXinjiang which are the main areas to plant cotton in ChinaAll the data are available from ldquoChina Statistics Yearbookrdquowhich is published by National Bureau of Statistics of Chinaand from ldquoAgricultural Costs and Benefitsrdquo which is editedby Chinarsquos National Development and Reform CommissionThe Malmquist index is solved and decomposed by softwareDEAP 21

32 Positive Results Figure 4 presents the results of Malm-quist index of Chinarsquos cotton production from 2001 to 2010Before the implementation of subsidy policy from 2001 to2006 the average annual growth rate of Malmquist indexwas 26 The Malmquist indices increased in most of yearsespecially increased up to 156 and 108 in 2001 and2006 than in 2000 and 2005 respectively At the same timeaccording to the decomposition results of Malmquist indexthe average annual value of technological change (Techch)increased by 47 (see Figure 5)

However after the implementation of the cotton seedsubsidy policy from 2007 the average annual values of

1156 107

0809

1076

0939

1108

0944 0918

1029 091

0

02

04

06

08

1

12

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 4 Chinarsquos cotton production Malmquist index

1257

1089

089

1081

0896

1068 1017 0921 0902 0849

0

02

04

06

08

1

12

14

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 5 Chinarsquos cotton production technological change

national Malmquist index decreased by 50 from 2007 to2010 Particularly in 2010 the decrease rate was up to 90The average annual changing rate of Techch was minus78 from2007 to 2010

In order to further test the change of cotton productivitywe continue calculating theMalmquist index and the techno-logical change of major provinces in China Figures 6 and 7report that all the provinces we selected were in the situationof declining Malmquist indices after the implementation ofseed subsidy (the details are shown in Table 1) From 2007to 2010 the average annual changing rates of Techch in theprovinces ofHebei Shandong Anhui Jiangxi Hubei Hunanand Xinjiang decreased 38 72 98 84 63 108and 21 respectively and the Malmquist indices decreased32 66 86 86 83 68 and 21 respectively

4 Conclusion and Policy Implications

41 Conclusion Subsidy is an important policy carried onthe agricultural department in many countries especiallyin developed countries However most literatures foundthat the subsidy could reduce instead of increasing theagricultural TFP There is the same phenomenon that existedin Chinarsquos cotton industry The output of Chinarsquos cotton hadbeen decreasing from 2008 to 2010 after implementing seedsubsidy policy in 2007This paper develops onemathematicalmodel to theoretically interpret what would happen about

6 Mathematical Problems in Engineering

Table 1 Chinarsquos cotton Malmquist index and technical change

Year 2001 2002 2003 2004 2005 2006 2001ndash2006 average 2007 2008 2009 2010 2007ndash2010 average

Country Malmquist index 1156 107 0809 1076 0939 1108 1026 0944 0918 1029 091 095Techch 1257 1089 089 1081 0896 1068 1047 1017 0921 0902 0849 0922

Hebei Malmquist index 0975 094 0899 0987 0911 1341 1009 1088 0931 0954 0898 0968Techch 0975 1133 0877 1077 0938 111 1018 1146 1025 0856 082 0962

ShandongMalmquist index 1055 0919 0902 0893 0987 1307 1011 0936 1001 0962 0835 0934Techch 1151 1108 0895 1066 0876 1115 1035 1065 0918 0897 0831 0928

Anhui Malmquist index 1354 1083 055 1201 077 1192 1025 1004 0712 1045 0896 0914Techch 1291 1083 0809 1047 0828 1077 1023 0923 0942 0909 0852 0907

Jiangxi Malmquist index 117 1097 0833 0967 1111 113 1051 0848 0883 1053 087 0914Techch 1513 1007 0754 1188 0814 1072 1058 0973 093 0938 0822 0916

Hubei Malmquist index 1678 1196 0868 0946 1135 1149 1162 0925 0978 0935 0831 0917Techch 1493 1142 0835 1239 0828 1149 1114 0925 1015 098 0826 0937

Hunan Malmquist index 1669 1306 0865 0848 0751 1275 1119 0802 0787 136 0777 0932Techch 125 1072 0865 1014 0826 1071 1016 0923 0903 0932 0808 0892

Xinjiang Malmquist index 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979Techch 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979

002040608

11214

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 6 Cotton Malmquist indices in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

the TFP after the subsidy policy was implemented Themodel indicates that TFP would be lower after the subsidywas implemented and there exists a negative relationshipbetween the subsidy policy andTFP if the subsidy is related toplanting area Using the input-output data of Chinarsquos cottonproduction this paper calculates theMalmquist index whichis the representative of the TFP and the technology progressof the whole country and major provinces from 2001 to 2010The conclusion is that the TFP of Chinarsquos cotton productiondecreased after seed subsidy was implemented from 2007not only in the whole country but also in major provincesin China So the seed subsidy policy has failed to effectivelyincrease the TFP of Chinarsquos cotton production

42 Policy Implications Thepositive conclusion of this papercould give us many important policy implications Firstlythe subsidy policy could not increase the agricultural TFP

0

02

04

06

08

1

12

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 7 Cotton technological changes in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

providing the subsidy related to the acreage Chinarsquos cottonseed subsidy is given to farmers according to their plantingarea the only one effect of the seed subsidy is to encouragefarmers to add acreage instead of adding other inputs andof course enlarging area is no means of increasing TFP Onthe contrary subsidy policy would breed inertia to farmersbecause farmers could get the subsidy from governmentas long as they plant cotton regardless how much yieldthey would harvest Secondly subsidy could be regarded asone kind of income which has the feature of stickiness aswage So the quantity of subsidy paid to farmers shouldbe increased constantly otherwise farmers would not besatisfied with the government From the above mentionedtwo aspects we could understand why there is a negativerelationship between the subsidy which is related to plantingarea and the productivity because the subsidy could notmotivate farmers to produce zealously and efficiently

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

Discrete MathematicsJournal of

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

to the multiobjective optimization model with discrete dataproposed in the references [17ndash22] Ding et al [17] establisheda model of multiobjective linear optimization and simulatedwhich subsidy could promote cotton production using thedata before 2007 and without subsidy in that period Theyconcluded that China should carry out multisubsidy insteadof seed subsidy such as subsidies for irrigation andmachines

Till now no literature explores the relationship betweensubsidy policy and productivity in theory and no literaturehas positively studied the relationship between subsidy policyand Chinarsquos cotton productivity This paper develops onemathematical model which theoretically demonstrates therule between the subsidies-related acreage and agriculturalTFP In order to verify the implication of the model thispaper will compare the TFP of Chinarsquos cotton productionbefore and after implementing the subsidy policy throughmeasuring Malmquist index The structure of this paper is asfollows Section 2 will derive and discuss one mathematicalmodelwhich investigates the theoretical relationship betweenthe seed subsidy and productivity Section 3 will make anempirical study of subsidy on Chinarsquos cotton TFP based onMalmquist index at last the paper will give the conclusionand some policy implications

2 A Theoretical Model

In order to observe what happened in Chinarsquos cotton produc-tivity after implementing seed subsidy we hereby establishtwo different profit functions

At first we consider the situation without subsidy Sup-posing farmerrsquos decision of planting cotton is based on priceso the planting area of cotton which reflects the producingdecision of farmers is a function of price

119878119897 = 119886 + 119887119901 (1)

119878119897 denotes the farmerrsquos planting area 119886 is a constant thatdenotes the initial planting area and 119901 denotes the price ofcotton The parameter 119887 is a marginal effect which reflects aunit change of 119878119897 upon119901 changing one unit and 119887 is a positivenumber which means that farmers will enlarge the plantingarea along with the price increasing

Suppose that yield is a Cobb-Douglas production func-tion in order to simplify the question we assume that laboris only one factor of input

119910 = 119864119897120572 (2)

Formula (2) describes the yield per unit planting area inwhich 119910 denotes the yield 119897 is the labor 120572 is the elasticity oflabor and 119864 is the labor efficiency which denotes the totalfactor productivity (TFP) in a certain So we get the profitfunction as follows

120587 = 119901119910119878119897 minus 1198620119878119897 (3)

In formula (3) 120587 denotes the profit and 1198620 denotes theproducing cost per mu Substitute 119878119897 and 119910 with formulas (1)and (2) respectively we can get the profit function as follows

120587 = 119901119864119897120572(119886 + 119887119901) minus 1198620 (119886 + 119887119901) (4)

Maximizing 120587 using first-order condition of function (3)with respect to 119901 equal to zero we can get the TFP function

119864 =1198620119887

(119886 + 2119887119901) 119897120572 (5)

Second we consider the farmerrsquos decision of producingunder the subsidy policy Chinarsquos cotton seed subsidy is 15Yuan per mu This kind of policy means the more area ofplanting cotton the more subsidies getting from governmentSo apparently Chinarsquos government wishes to increase thecotton production through stimulating farmers to enlargetheir cotton planting area using subsidy Then the plantingarea is certainly a function of subsidy

119878119897 = 119886 + 119887119901 + 119888119878119887 (6)

119878119887 denotes the subsidy and the parameter of 119888 is positive thatmeanswhen the subsidy paid to the farmers the planting areawill be increased which conforms the governmentrsquos wish

So we get another profit function as follows

120587 = 119901119910119878119897 + 119878119887119878119897 minus 1198620119878119897 (7)

Define 119910 = 119864119904119897120572 in formula (7) so Maximizing 120587 using

first-order condition of function (7) with respect to 119901 equalto zero and substituting 119878119897 with formula (6) we can get the119864119904 (the TFP after subsidy is carried out) as follows

119864119904 =1198620119887

(119886 + 2119887119901) 119897120572minus

(119887 + 119888) 119878119887

(119886 + 2119887119901) 119897120572 (8)

Apparently 119864119904 lt 119864 because (119887 + 119888)119878119887(119886 + 2119887119901)119897120572gt 0

So the TFP will be lower after the subsidy and there is anegative relationship between the TFP and the subsidy Theabove theoretical model reveals that the agricultural TFP willdecline when subsidy is implemented if the subsidy is relatedto planting area

3 Measuring Chinarsquos Cotton TFP

31 Model and Data Since the late 1990s Malmquist indexbased on Data Envelopment Analysis (DEA) method hasbeen widely used to measure and decompose the TFP andit is convenient to apply DEA techniques to capture the effectof the technical inefficiency [18] Malmquist index was putforward in 1953 by Malmquist [19] the Swedish economistand statistician and then Caves et al [20] and Fare et al [21]developed Malmquist index to measure TFP

311 Definition and Decomposition of the Malmquist IndexMalmquist index is a ratio of distance function in differentperiods The distance function is a technical one with multi-input andmultioutput without any assumptions in producerrsquosbehavior

Assuming that 119883 is a 119881-dimensional vector of inputfactors 119884 is 119882-dimensional vector of output and 119874(119883)denotes the set of output which is bounded closed and

4 Mathematical Problems in Engineering

convex According to Shepherd [22] the output distancefunction119863119900(119883 119884) on the bases of 119874(119883) is as follows

119863119900 (119883 119884) = Min120601 (119884120601) isin 119874 (119883) (9)

Let (119883119905119900 119884119905

119900) and (119883119905+119894

119900 119884119905+119894

119900) denote the input and output

vectors respectively in period 119905 and 119905 + 119894 119863119905119900(119883119905

119900 119884119905

119900) is the

output distance function based on the technology in period119905 119863119905119900(119883119905+119894

119900 119884119905+119894

119900) is the output distance function in 119905 + 119894 with

the technology in 119905If the technology changed from period 119905 to 119905 + 119894 the

Malmquist index in respect of output in period of 119905 is asfollows

119872119905

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900) (10)

Similarly the Malmquist index on the respect of outputin period 119905 + 119894 is as follows

119872119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900) (11)

Fare et al [21] adopted geometric mean of Malmquistindex in two periods as the definition in order to avoid errorsexisted in different periods which are selected random

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

(12)

Malmquist index could be decomposed as follows

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

=

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)

times [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905+119894119900 119884119905+119894119900)times119863119905

119900(119883119905

119900 119884119905

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

= Ech119900 times Tch119900(13)

where Ech119900 and Tch119900 denote the efficiency change and thetechnical change from period 119905 to period 119905 + 119894 respectively

Usually Malmquist Index could be gotten by DEAmethod DEA is the nonparametric mathematical program-ming approach to frontier estimation Assume that there aredata on 119870 inputs and 119872 outputs on each of 119873 decisionmaking units (DMUs) The 119870 times 119873 input matrix 119883 and

the 119872 times 119873 output matrix 119884 represent the data of all 119873DMUs The purpose of DEA is to construct a nonparametricenvelopment frontier over the data points such that allobserved points lie on or below the production frontierFor each DMU we would like to obtain a measure of theratio of all outputs over all inputs such as where 119906 is an119872 times 1 vector of output weights and V is a 119870 times 1 vectorof input weights To select optimal weights we specify themathematical programming problem

Max119906V

(1199061015840119910119894

V1015840119909119894)

st

1199061015840119910119895

V1015840119909119895le 1 119895 = 1 2 119873

119906 V ge 0

(14)

In order to avoid an infinite number of solutions impos-ing V1015840119909119895 = 1 and using the duality in linear programming

we can derive an equivalent envelopment form as follows

Min120579120582

120579

st

minus119910119894 + 119884120582 ge 0

120579119909119894 minus 119883120582 ge 0

120582 ge 0

(15)

where 120579 is a scalar standing for the efficiency score for the119894th DMU It will satisfy 120579 le 1 with a value of 1 indicating apoint on the frontier and hence a technically efficient DMUSo calculating Malmquist Index in any adjacent two years(119894 = 0 1) equal to solving the DEA model of the followingfour distance functions

[119863119905

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905+1

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905+1

119900

120579119895 ge 0 119895 = 1 2 119873

Mathematical Problems in Engineering 5

[119863119905

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

119873

sum

119895=1

120579119895 = 1 120579119895 ge 0 119895 = 1 2 119873

(16)

In the above models 119883 denotes input vectors 119884 denotesoutput vectors 120601 (0 lt 120601 lt 1) is a scalar which denotes theefficiency of technology of 119895 decision-making unit under thecondition of constant return to scale and 119895 = 1 2 119873 120579119895is a constant vector

312 Data Description The importance of nonparametricMalmquist index analysis is that the selected variables shouldreflect the input and output of cotton production perfectlyWe will use the labor values (standard working day) directmaterial costs and overhead expenses per mu as the inputfactors and cotton yield per mu as the output In order to getthe accurate conclusion we will measure the TFP of Chinarsquoscotton production not only for the whole country but alsofor every major producing cotton province So we choosethe input-output data of the whole nation and provincesof Hebei Shandong Anhui Jiangxi Hubei Hunan andXinjiang which are the main areas to plant cotton in ChinaAll the data are available from ldquoChina Statistics Yearbookrdquowhich is published by National Bureau of Statistics of Chinaand from ldquoAgricultural Costs and Benefitsrdquo which is editedby Chinarsquos National Development and Reform CommissionThe Malmquist index is solved and decomposed by softwareDEAP 21

32 Positive Results Figure 4 presents the results of Malm-quist index of Chinarsquos cotton production from 2001 to 2010Before the implementation of subsidy policy from 2001 to2006 the average annual growth rate of Malmquist indexwas 26 The Malmquist indices increased in most of yearsespecially increased up to 156 and 108 in 2001 and2006 than in 2000 and 2005 respectively At the same timeaccording to the decomposition results of Malmquist indexthe average annual value of technological change (Techch)increased by 47 (see Figure 5)

However after the implementation of the cotton seedsubsidy policy from 2007 the average annual values of

1156 107

0809

1076

0939

1108

0944 0918

1029 091

0

02

04

06

08

1

12

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 4 Chinarsquos cotton production Malmquist index

1257

1089

089

1081

0896

1068 1017 0921 0902 0849

0

02

04

06

08

1

12

14

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 5 Chinarsquos cotton production technological change

national Malmquist index decreased by 50 from 2007 to2010 Particularly in 2010 the decrease rate was up to 90The average annual changing rate of Techch was minus78 from2007 to 2010

In order to further test the change of cotton productivitywe continue calculating theMalmquist index and the techno-logical change of major provinces in China Figures 6 and 7report that all the provinces we selected were in the situationof declining Malmquist indices after the implementation ofseed subsidy (the details are shown in Table 1) From 2007to 2010 the average annual changing rates of Techch in theprovinces ofHebei Shandong Anhui Jiangxi Hubei Hunanand Xinjiang decreased 38 72 98 84 63 108and 21 respectively and the Malmquist indices decreased32 66 86 86 83 68 and 21 respectively

4 Conclusion and Policy Implications

41 Conclusion Subsidy is an important policy carried onthe agricultural department in many countries especiallyin developed countries However most literatures foundthat the subsidy could reduce instead of increasing theagricultural TFP There is the same phenomenon that existedin Chinarsquos cotton industry The output of Chinarsquos cotton hadbeen decreasing from 2008 to 2010 after implementing seedsubsidy policy in 2007This paper develops onemathematicalmodel to theoretically interpret what would happen about

6 Mathematical Problems in Engineering

Table 1 Chinarsquos cotton Malmquist index and technical change

Year 2001 2002 2003 2004 2005 2006 2001ndash2006 average 2007 2008 2009 2010 2007ndash2010 average

Country Malmquist index 1156 107 0809 1076 0939 1108 1026 0944 0918 1029 091 095Techch 1257 1089 089 1081 0896 1068 1047 1017 0921 0902 0849 0922

Hebei Malmquist index 0975 094 0899 0987 0911 1341 1009 1088 0931 0954 0898 0968Techch 0975 1133 0877 1077 0938 111 1018 1146 1025 0856 082 0962

ShandongMalmquist index 1055 0919 0902 0893 0987 1307 1011 0936 1001 0962 0835 0934Techch 1151 1108 0895 1066 0876 1115 1035 1065 0918 0897 0831 0928

Anhui Malmquist index 1354 1083 055 1201 077 1192 1025 1004 0712 1045 0896 0914Techch 1291 1083 0809 1047 0828 1077 1023 0923 0942 0909 0852 0907

Jiangxi Malmquist index 117 1097 0833 0967 1111 113 1051 0848 0883 1053 087 0914Techch 1513 1007 0754 1188 0814 1072 1058 0973 093 0938 0822 0916

Hubei Malmquist index 1678 1196 0868 0946 1135 1149 1162 0925 0978 0935 0831 0917Techch 1493 1142 0835 1239 0828 1149 1114 0925 1015 098 0826 0937

Hunan Malmquist index 1669 1306 0865 0848 0751 1275 1119 0802 0787 136 0777 0932Techch 125 1072 0865 1014 0826 1071 1016 0923 0903 0932 0808 0892

Xinjiang Malmquist index 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979Techch 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979

002040608

11214

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 6 Cotton Malmquist indices in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

the TFP after the subsidy policy was implemented Themodel indicates that TFP would be lower after the subsidywas implemented and there exists a negative relationshipbetween the subsidy policy andTFP if the subsidy is related toplanting area Using the input-output data of Chinarsquos cottonproduction this paper calculates theMalmquist index whichis the representative of the TFP and the technology progressof the whole country and major provinces from 2001 to 2010The conclusion is that the TFP of Chinarsquos cotton productiondecreased after seed subsidy was implemented from 2007not only in the whole country but also in major provincesin China So the seed subsidy policy has failed to effectivelyincrease the TFP of Chinarsquos cotton production

42 Policy Implications Thepositive conclusion of this papercould give us many important policy implications Firstlythe subsidy policy could not increase the agricultural TFP

0

02

04

06

08

1

12

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 7 Cotton technological changes in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

providing the subsidy related to the acreage Chinarsquos cottonseed subsidy is given to farmers according to their plantingarea the only one effect of the seed subsidy is to encouragefarmers to add acreage instead of adding other inputs andof course enlarging area is no means of increasing TFP Onthe contrary subsidy policy would breed inertia to farmersbecause farmers could get the subsidy from governmentas long as they plant cotton regardless how much yieldthey would harvest Secondly subsidy could be regarded asone kind of income which has the feature of stickiness aswage So the quantity of subsidy paid to farmers shouldbe increased constantly otherwise farmers would not besatisfied with the government From the above mentionedtwo aspects we could understand why there is a negativerelationship between the subsidy which is related to plantingarea and the productivity because the subsidy could notmotivate farmers to produce zealously and efficiently

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

convex According to Shepherd [22] the output distancefunction119863119900(119883 119884) on the bases of 119874(119883) is as follows

119863119900 (119883 119884) = Min120601 (119884120601) isin 119874 (119883) (9)

Let (119883119905119900 119884119905

119900) and (119883119905+119894

119900 119884119905+119894

119900) denote the input and output

vectors respectively in period 119905 and 119905 + 119894 119863119905119900(119883119905

119900 119884119905

119900) is the

output distance function based on the technology in period119905 119863119905119900(119883119905+119894

119900 119884119905+119894

119900) is the output distance function in 119905 + 119894 with

the technology in 119905If the technology changed from period 119905 to 119905 + 119894 the

Malmquist index in respect of output in period of 119905 is asfollows

119872119905

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900) (10)

Similarly the Malmquist index on the respect of outputin period 119905 + 119894 is as follows

119872119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900) =

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900) (11)

Fare et al [21] adopted geometric mean of Malmquistindex in two periods as the definition in order to avoid errorsexisted in different periods which are selected random

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

(12)

Malmquist index could be decomposed as follows

119872119900 (119883119905+119894

119900 119884119905+119894

119900 119883119905

119900 119884119905

119900)

= [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)] times [

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

=

119863119905+119894

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905119900(119883119905119900 119884119905119900)

times [

119863119905

119900(119883119905+119894

119900 119884119905+119894

119900)

119863119905+119894119900(119883119905+119894119900 119884119905+119894119900)times119863119905

119900(119883119905

119900 119884119905

119900)

119863119905+119894119900(119883119905119900 119884119905119900)]

12

= Ech119900 times Tch119900(13)

where Ech119900 and Tch119900 denote the efficiency change and thetechnical change from period 119905 to period 119905 + 119894 respectively

Usually Malmquist Index could be gotten by DEAmethod DEA is the nonparametric mathematical program-ming approach to frontier estimation Assume that there aredata on 119870 inputs and 119872 outputs on each of 119873 decisionmaking units (DMUs) The 119870 times 119873 input matrix 119883 and

the 119872 times 119873 output matrix 119884 represent the data of all 119873DMUs The purpose of DEA is to construct a nonparametricenvelopment frontier over the data points such that allobserved points lie on or below the production frontierFor each DMU we would like to obtain a measure of theratio of all outputs over all inputs such as where 119906 is an119872 times 1 vector of output weights and V is a 119870 times 1 vectorof input weights To select optimal weights we specify themathematical programming problem

Max119906V

(1199061015840119910119894

V1015840119909119894)

st

1199061015840119910119895

V1015840119909119895le 1 119895 = 1 2 119873

119906 V ge 0

(14)

In order to avoid an infinite number of solutions impos-ing V1015840119909119895 = 1 and using the duality in linear programming

we can derive an equivalent envelopment form as follows

Min120579120582

120579

st

minus119910119894 + 119884120582 ge 0

120579119909119894 minus 119883120582 ge 0

120582 ge 0

(15)

where 120579 is a scalar standing for the efficiency score for the119894th DMU It will satisfy 120579 le 1 with a value of 1 indicating apoint on the frontier and hence a technically efficient DMUSo calculating Malmquist Index in any adjacent two years(119894 = 0 1) equal to solving the DEA model of the followingfour distance functions

[119863119905

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905+1

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905+1

119900

120579119895 ge 0 119895 = 1 2 119873

Mathematical Problems in Engineering 5

[119863119905

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

119873

sum

119895=1

120579119895 = 1 120579119895 ge 0 119895 = 1 2 119873

(16)

In the above models 119883 denotes input vectors 119884 denotesoutput vectors 120601 (0 lt 120601 lt 1) is a scalar which denotes theefficiency of technology of 119895 decision-making unit under thecondition of constant return to scale and 119895 = 1 2 119873 120579119895is a constant vector

312 Data Description The importance of nonparametricMalmquist index analysis is that the selected variables shouldreflect the input and output of cotton production perfectlyWe will use the labor values (standard working day) directmaterial costs and overhead expenses per mu as the inputfactors and cotton yield per mu as the output In order to getthe accurate conclusion we will measure the TFP of Chinarsquoscotton production not only for the whole country but alsofor every major producing cotton province So we choosethe input-output data of the whole nation and provincesof Hebei Shandong Anhui Jiangxi Hubei Hunan andXinjiang which are the main areas to plant cotton in ChinaAll the data are available from ldquoChina Statistics Yearbookrdquowhich is published by National Bureau of Statistics of Chinaand from ldquoAgricultural Costs and Benefitsrdquo which is editedby Chinarsquos National Development and Reform CommissionThe Malmquist index is solved and decomposed by softwareDEAP 21

32 Positive Results Figure 4 presents the results of Malm-quist index of Chinarsquos cotton production from 2001 to 2010Before the implementation of subsidy policy from 2001 to2006 the average annual growth rate of Malmquist indexwas 26 The Malmquist indices increased in most of yearsespecially increased up to 156 and 108 in 2001 and2006 than in 2000 and 2005 respectively At the same timeaccording to the decomposition results of Malmquist indexthe average annual value of technological change (Techch)increased by 47 (see Figure 5)

However after the implementation of the cotton seedsubsidy policy from 2007 the average annual values of

1156 107

0809

1076

0939

1108

0944 0918

1029 091

0

02

04

06

08

1

12

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 4 Chinarsquos cotton production Malmquist index

1257

1089

089

1081

0896

1068 1017 0921 0902 0849

0

02

04

06

08

1

12

14

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 5 Chinarsquos cotton production technological change

national Malmquist index decreased by 50 from 2007 to2010 Particularly in 2010 the decrease rate was up to 90The average annual changing rate of Techch was minus78 from2007 to 2010

In order to further test the change of cotton productivitywe continue calculating theMalmquist index and the techno-logical change of major provinces in China Figures 6 and 7report that all the provinces we selected were in the situationof declining Malmquist indices after the implementation ofseed subsidy (the details are shown in Table 1) From 2007to 2010 the average annual changing rates of Techch in theprovinces ofHebei Shandong Anhui Jiangxi Hubei Hunanand Xinjiang decreased 38 72 98 84 63 108and 21 respectively and the Malmquist indices decreased32 66 86 86 83 68 and 21 respectively

4 Conclusion and Policy Implications

41 Conclusion Subsidy is an important policy carried onthe agricultural department in many countries especiallyin developed countries However most literatures foundthat the subsidy could reduce instead of increasing theagricultural TFP There is the same phenomenon that existedin Chinarsquos cotton industry The output of Chinarsquos cotton hadbeen decreasing from 2008 to 2010 after implementing seedsubsidy policy in 2007This paper develops onemathematicalmodel to theoretically interpret what would happen about

6 Mathematical Problems in Engineering

Table 1 Chinarsquos cotton Malmquist index and technical change

Year 2001 2002 2003 2004 2005 2006 2001ndash2006 average 2007 2008 2009 2010 2007ndash2010 average

Country Malmquist index 1156 107 0809 1076 0939 1108 1026 0944 0918 1029 091 095Techch 1257 1089 089 1081 0896 1068 1047 1017 0921 0902 0849 0922

Hebei Malmquist index 0975 094 0899 0987 0911 1341 1009 1088 0931 0954 0898 0968Techch 0975 1133 0877 1077 0938 111 1018 1146 1025 0856 082 0962

ShandongMalmquist index 1055 0919 0902 0893 0987 1307 1011 0936 1001 0962 0835 0934Techch 1151 1108 0895 1066 0876 1115 1035 1065 0918 0897 0831 0928

Anhui Malmquist index 1354 1083 055 1201 077 1192 1025 1004 0712 1045 0896 0914Techch 1291 1083 0809 1047 0828 1077 1023 0923 0942 0909 0852 0907

Jiangxi Malmquist index 117 1097 0833 0967 1111 113 1051 0848 0883 1053 087 0914Techch 1513 1007 0754 1188 0814 1072 1058 0973 093 0938 0822 0916

Hubei Malmquist index 1678 1196 0868 0946 1135 1149 1162 0925 0978 0935 0831 0917Techch 1493 1142 0835 1239 0828 1149 1114 0925 1015 098 0826 0937

Hunan Malmquist index 1669 1306 0865 0848 0751 1275 1119 0802 0787 136 0777 0932Techch 125 1072 0865 1014 0826 1071 1016 0923 0903 0932 0808 0892

Xinjiang Malmquist index 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979Techch 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979

002040608

11214

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 6 Cotton Malmquist indices in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

the TFP after the subsidy policy was implemented Themodel indicates that TFP would be lower after the subsidywas implemented and there exists a negative relationshipbetween the subsidy policy andTFP if the subsidy is related toplanting area Using the input-output data of Chinarsquos cottonproduction this paper calculates theMalmquist index whichis the representative of the TFP and the technology progressof the whole country and major provinces from 2001 to 2010The conclusion is that the TFP of Chinarsquos cotton productiondecreased after seed subsidy was implemented from 2007not only in the whole country but also in major provincesin China So the seed subsidy policy has failed to effectivelyincrease the TFP of Chinarsquos cotton production

42 Policy Implications Thepositive conclusion of this papercould give us many important policy implications Firstlythe subsidy policy could not increase the agricultural TFP

0

02

04

06

08

1

12

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 7 Cotton technological changes in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

providing the subsidy related to the acreage Chinarsquos cottonseed subsidy is given to farmers according to their plantingarea the only one effect of the seed subsidy is to encouragefarmers to add acreage instead of adding other inputs andof course enlarging area is no means of increasing TFP Onthe contrary subsidy policy would breed inertia to farmersbecause farmers could get the subsidy from governmentas long as they plant cotton regardless how much yieldthey would harvest Secondly subsidy could be regarded asone kind of income which has the feature of stickiness aswage So the quantity of subsidy paid to farmers shouldbe increased constantly otherwise farmers would not besatisfied with the government From the above mentionedtwo aspects we could understand why there is a negativerelationship between the subsidy which is related to plantingarea and the productivity because the subsidy could notmotivate farmers to produce zealously and efficiently

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

[119863119905

119900(119883119905+1

119900 119884119905+1

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

120579119895 ge 0 119895 = 1 2 119873

[119863119905+1

119900(119883119905

119900 119884119905

119900)]minus1

= Max120601

st

119873

sum

119895=1

120579119895119883119905+1

119900119895le 119883119905

119900

119873

sum

119895=1

120579119895119884119905+1

119900119895ge 120601119884119905

119900

119873

sum

119895=1

120579119895 = 1 120579119895 ge 0 119895 = 1 2 119873

(16)

In the above models 119883 denotes input vectors 119884 denotesoutput vectors 120601 (0 lt 120601 lt 1) is a scalar which denotes theefficiency of technology of 119895 decision-making unit under thecondition of constant return to scale and 119895 = 1 2 119873 120579119895is a constant vector

312 Data Description The importance of nonparametricMalmquist index analysis is that the selected variables shouldreflect the input and output of cotton production perfectlyWe will use the labor values (standard working day) directmaterial costs and overhead expenses per mu as the inputfactors and cotton yield per mu as the output In order to getthe accurate conclusion we will measure the TFP of Chinarsquoscotton production not only for the whole country but alsofor every major producing cotton province So we choosethe input-output data of the whole nation and provincesof Hebei Shandong Anhui Jiangxi Hubei Hunan andXinjiang which are the main areas to plant cotton in ChinaAll the data are available from ldquoChina Statistics Yearbookrdquowhich is published by National Bureau of Statistics of Chinaand from ldquoAgricultural Costs and Benefitsrdquo which is editedby Chinarsquos National Development and Reform CommissionThe Malmquist index is solved and decomposed by softwareDEAP 21

32 Positive Results Figure 4 presents the results of Malm-quist index of Chinarsquos cotton production from 2001 to 2010Before the implementation of subsidy policy from 2001 to2006 the average annual growth rate of Malmquist indexwas 26 The Malmquist indices increased in most of yearsespecially increased up to 156 and 108 in 2001 and2006 than in 2000 and 2005 respectively At the same timeaccording to the decomposition results of Malmquist indexthe average annual value of technological change (Techch)increased by 47 (see Figure 5)

However after the implementation of the cotton seedsubsidy policy from 2007 the average annual values of

1156 107

0809

1076

0939

1108

0944 0918

1029 091

0

02

04

06

08

1

12

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 4 Chinarsquos cotton production Malmquist index

1257

1089

089

1081

0896

1068 1017 0921 0902 0849

0

02

04

06

08

1

12

14

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 5 Chinarsquos cotton production technological change

national Malmquist index decreased by 50 from 2007 to2010 Particularly in 2010 the decrease rate was up to 90The average annual changing rate of Techch was minus78 from2007 to 2010

In order to further test the change of cotton productivitywe continue calculating theMalmquist index and the techno-logical change of major provinces in China Figures 6 and 7report that all the provinces we selected were in the situationof declining Malmquist indices after the implementation ofseed subsidy (the details are shown in Table 1) From 2007to 2010 the average annual changing rates of Techch in theprovinces ofHebei Shandong Anhui Jiangxi Hubei Hunanand Xinjiang decreased 38 72 98 84 63 108and 21 respectively and the Malmquist indices decreased32 66 86 86 83 68 and 21 respectively

4 Conclusion and Policy Implications

41 Conclusion Subsidy is an important policy carried onthe agricultural department in many countries especiallyin developed countries However most literatures foundthat the subsidy could reduce instead of increasing theagricultural TFP There is the same phenomenon that existedin Chinarsquos cotton industry The output of Chinarsquos cotton hadbeen decreasing from 2008 to 2010 after implementing seedsubsidy policy in 2007This paper develops onemathematicalmodel to theoretically interpret what would happen about

6 Mathematical Problems in Engineering

Table 1 Chinarsquos cotton Malmquist index and technical change

Year 2001 2002 2003 2004 2005 2006 2001ndash2006 average 2007 2008 2009 2010 2007ndash2010 average

Country Malmquist index 1156 107 0809 1076 0939 1108 1026 0944 0918 1029 091 095Techch 1257 1089 089 1081 0896 1068 1047 1017 0921 0902 0849 0922

Hebei Malmquist index 0975 094 0899 0987 0911 1341 1009 1088 0931 0954 0898 0968Techch 0975 1133 0877 1077 0938 111 1018 1146 1025 0856 082 0962

ShandongMalmquist index 1055 0919 0902 0893 0987 1307 1011 0936 1001 0962 0835 0934Techch 1151 1108 0895 1066 0876 1115 1035 1065 0918 0897 0831 0928

Anhui Malmquist index 1354 1083 055 1201 077 1192 1025 1004 0712 1045 0896 0914Techch 1291 1083 0809 1047 0828 1077 1023 0923 0942 0909 0852 0907

Jiangxi Malmquist index 117 1097 0833 0967 1111 113 1051 0848 0883 1053 087 0914Techch 1513 1007 0754 1188 0814 1072 1058 0973 093 0938 0822 0916

Hubei Malmquist index 1678 1196 0868 0946 1135 1149 1162 0925 0978 0935 0831 0917Techch 1493 1142 0835 1239 0828 1149 1114 0925 1015 098 0826 0937

Hunan Malmquist index 1669 1306 0865 0848 0751 1275 1119 0802 0787 136 0777 0932Techch 125 1072 0865 1014 0826 1071 1016 0923 0903 0932 0808 0892

Xinjiang Malmquist index 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979Techch 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979

002040608

11214

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 6 Cotton Malmquist indices in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

the TFP after the subsidy policy was implemented Themodel indicates that TFP would be lower after the subsidywas implemented and there exists a negative relationshipbetween the subsidy policy andTFP if the subsidy is related toplanting area Using the input-output data of Chinarsquos cottonproduction this paper calculates theMalmquist index whichis the representative of the TFP and the technology progressof the whole country and major provinces from 2001 to 2010The conclusion is that the TFP of Chinarsquos cotton productiondecreased after seed subsidy was implemented from 2007not only in the whole country but also in major provincesin China So the seed subsidy policy has failed to effectivelyincrease the TFP of Chinarsquos cotton production

42 Policy Implications Thepositive conclusion of this papercould give us many important policy implications Firstlythe subsidy policy could not increase the agricultural TFP

0

02

04

06

08

1

12

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 7 Cotton technological changes in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

providing the subsidy related to the acreage Chinarsquos cottonseed subsidy is given to farmers according to their plantingarea the only one effect of the seed subsidy is to encouragefarmers to add acreage instead of adding other inputs andof course enlarging area is no means of increasing TFP Onthe contrary subsidy policy would breed inertia to farmersbecause farmers could get the subsidy from governmentas long as they plant cotton regardless how much yieldthey would harvest Secondly subsidy could be regarded asone kind of income which has the feature of stickiness aswage So the quantity of subsidy paid to farmers shouldbe increased constantly otherwise farmers would not besatisfied with the government From the above mentionedtwo aspects we could understand why there is a negativerelationship between the subsidy which is related to plantingarea and the productivity because the subsidy could notmotivate farmers to produce zealously and efficiently

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Table 1 Chinarsquos cotton Malmquist index and technical change

Year 2001 2002 2003 2004 2005 2006 2001ndash2006 average 2007 2008 2009 2010 2007ndash2010 average

Country Malmquist index 1156 107 0809 1076 0939 1108 1026 0944 0918 1029 091 095Techch 1257 1089 089 1081 0896 1068 1047 1017 0921 0902 0849 0922

Hebei Malmquist index 0975 094 0899 0987 0911 1341 1009 1088 0931 0954 0898 0968Techch 0975 1133 0877 1077 0938 111 1018 1146 1025 0856 082 0962

ShandongMalmquist index 1055 0919 0902 0893 0987 1307 1011 0936 1001 0962 0835 0934Techch 1151 1108 0895 1066 0876 1115 1035 1065 0918 0897 0831 0928

Anhui Malmquist index 1354 1083 055 1201 077 1192 1025 1004 0712 1045 0896 0914Techch 1291 1083 0809 1047 0828 1077 1023 0923 0942 0909 0852 0907

Jiangxi Malmquist index 117 1097 0833 0967 1111 113 1051 0848 0883 1053 087 0914Techch 1513 1007 0754 1188 0814 1072 1058 0973 093 0938 0822 0916

Hubei Malmquist index 1678 1196 0868 0946 1135 1149 1162 0925 0978 0935 0831 0917Techch 1493 1142 0835 1239 0828 1149 1114 0925 1015 098 0826 0937

Hunan Malmquist index 1669 1306 0865 0848 0751 1275 1119 0802 0787 136 0777 0932Techch 125 1072 0865 1014 0826 1071 1016 0923 0903 0932 0808 0892

Xinjiang Malmquist index 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979Techch 0918 1209 0968 0968 1101 1059 1037 0964 0983 1048 0921 0979

002040608

11214

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 6 Cotton Malmquist indices in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

the TFP after the subsidy policy was implemented Themodel indicates that TFP would be lower after the subsidywas implemented and there exists a negative relationshipbetween the subsidy policy andTFP if the subsidy is related toplanting area Using the input-output data of Chinarsquos cottonproduction this paper calculates theMalmquist index whichis the representative of the TFP and the technology progressof the whole country and major provinces from 2001 to 2010The conclusion is that the TFP of Chinarsquos cotton productiondecreased after seed subsidy was implemented from 2007not only in the whole country but also in major provincesin China So the seed subsidy policy has failed to effectivelyincrease the TFP of Chinarsquos cotton production

42 Policy Implications Thepositive conclusion of this papercould give us many important policy implications Firstlythe subsidy policy could not increase the agricultural TFP

0

02

04

06

08

1

12

HEB SHD ANH JIX HUB HUN XIJ

2001ndash2006 average2007ndash2010 average

Figure 7 Cotton technological changes in Chinarsquos major provinceNotes HEB SHD ANH JIX HUB HUN and XIJ respectivelyrepresent the provinces of Hebei Shandong Anhui Jiangxi HubeiHunan and Xinjiang

providing the subsidy related to the acreage Chinarsquos cottonseed subsidy is given to farmers according to their plantingarea the only one effect of the seed subsidy is to encouragefarmers to add acreage instead of adding other inputs andof course enlarging area is no means of increasing TFP Onthe contrary subsidy policy would breed inertia to farmersbecause farmers could get the subsidy from governmentas long as they plant cotton regardless how much yieldthey would harvest Secondly subsidy could be regarded asone kind of income which has the feature of stickiness aswage So the quantity of subsidy paid to farmers shouldbe increased constantly otherwise farmers would not besatisfied with the government From the above mentionedtwo aspects we could understand why there is a negativerelationship between the subsidy which is related to plantingarea and the productivity because the subsidy could notmotivate farmers to produce zealously and efficiently

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Agriculture is a weak industry which is often influencedby the natural and economic environment Because thesupplying elasticity is generally higher than the demandingelasticity agricultural production would be always in hugefluctuation without any intervention Subsidy policy is oneof the government intervening measures which could keepstable agricultural production and market But if the gov-ernment wants to encourage farmers to improve agriculturalproductivity through the subsidy policy they would get theopposite result because the subsidy policy has no functionto increase the TFP as this paper indicated as long assubsidy is related to the acreage So in order to increasethe agricultural TFP promoting the investment in researchand development of agriculture and enhancing the technicalprogress in agriculture would be a better way than the subsidypolicy

43 Further Discussion This paper makes a significantwork in studying agricultural subsidy policy especially ininterpreting the relation between the subsidy policy andagricultural TFP through developing a theoretical model Butthere are lots of interesting works should be developed Firstthe mathematical model induced in this paper is under thesupposition of subsidy related to the acreage If looseningthe assumption which kind of relationship exists betweenthe subsidy policy and agricultural TFP should be furtherinvestigated Second this paper only tests Chinarsquos cottonproduction using Malmquist index but other agricultureproducts such as rice wheat soybean maize and porkshould be also needed tomeasure so as to efficiently verify themodel So we will continue to extend the model and apply itin many agricultural productions not only in China but alsoinUSA EU Japan and so forth so as to perfect themodel andobtain much more policy significance

Authorsrsquo Contribution

Y W Tan conceived and developed the mathematical modeland wrote the paper J B Guan Collected the data Measuredthe Malmquist index using the software DEAP 21 H RKarimi Perfected analyzed and corrected the paper

Acknowledgments

The authors gratefully acknowledge the two anonymousreferees for their helpful suggestions and corrections onthe draft of our paper which improved the contents Thispaper is the initial results of the National Natural ScienceFoundation of China (70873043) and Guangdong ProvincialSocial Science Fund Project (09E-17) Guangdong ProvinceEducational Department Research Project (11ZGXM79003)the Program for New Century Excellent Talents in ChineseUniversity

References

[1] K Giannakas R Schoney and V Tzouvelekas ldquoTechnical effi-ciency technological change and output growth of wheat farms

in Saskatchewanrdquo Canadian Journal of Agricultural Economicsvol 49 no 2 pp 135ndash152 2001

[2] A Rezitis K Tsiboukas and S Tsoukalas ldquoInvestigationof factors influencing the technical efficiency of agriculturalproducers participating in farm credit programs the case ofGreecerdquo Journal of Agricultural and Applied Economics vol 35no 3 pp 529ndash541 2003

[3] H Guyomard L Latruffe and C Le Mouel ldquoTechnical effi-ciency technical progress and productivity change in Frenchagriculture Do subsidies and farmsrsquo sizematterrdquo inProceedingsof the 96th European Association of Agricultural EconomistsSeminar (EAAE rsquo06) Tanikon Switzerland January 2006

[4] M Sabir and QM Ahmed ldquoEconomic reforms and total factorproductivity growth in Pakistan an empirical analysisrdquoBusinessReview vol 3 no 1 pp 53ndash68 2008

[5] O Nivievskyi ldquoPrice support efficiency and technology changeof Ukrainian dairy farms spatial dependence in the compo-nents of productivity growthrdquo inProceedings of the InternationalAssociation of Agricultural Economists Conference BeijingChina August 2009

[6] L Latruffe H Guyomard and C Le Mouel ldquoThe role ofpublic subsidies on farmsrsquo managerial efficiency an applicationof a five-stage approach to Francerdquo Working Paper SMART-LERECO 09-05 2009

[7] S Mary ldquoAssessing the Impacts of Pillar 1 and 2 Subsidies onTFP in French Crop Farmsrdquo Journal of Agricultural Economicsvol 64 no 1 pp 133ndash144 2013

[8] A Kazukauskas and C Newman ldquoCAP reform and its impacton structural change and productivity growth a cross countryanalysisrdquo in Proceedings of the 114th European Associationof Agricultural Economists Seminar on Structural Change inAgriculture (EAAE rsquo10) Berlin Germany April 2010

[9] M Rizov J Pokrivcak and P Ciaian ldquoCAP subsidies andproductivity of the EU farmsrdquo inProceedings of the InternationalAssociation of Agricultural Economists (IAAE) Triennial Confer-ence Foz do Iguacu Brazil August 2012

[10] B Chen and Y Wang ldquoInvestigation and analysis on GrainSubsidy reform in Hubei provincerdquo Economic Problems vol 3pp 50ndash52 2006

[11] R Zhao and Q Meng ldquoAnalysis on the direct subsidy policyeffect on Grain production-a case of Shandong provincerdquoAgriculture Economic vol 5 pp 20ndash21 2012

[12] J Wang and H Xiao ldquoEffect analysis on the policy of improvedvariety subsidy agricultural machine subsidy and reduction orremission of agricultural Taxes in Chinardquo Issues in AgriculturalEconomy vol 2 pp 24ndash28 2007

[13] Z Cao and T Zhang ldquoEfficient analysis on the allowancefor purchasing agricultural machinery and Peasantrsquos increasedincomerdquo Journal of AgriculturalMechanization Research vol 12pp 67ndash69 2006

[14] L Lu ldquoThe prospective performance analysis of agriculturesubsidy policy-a survey of farmer families in Shengchi CountyrdquoReformation and Strategy vol 8 pp 68ndash71 2006

[15] S Fang and W Wang ldquoStudy on agricultural subsidy policy inthe context of soaring costrdquo Management World vol 9 pp 91ndash108 2009

[16] L Wu and W Lu ldquoSimulation study on the performance ofGrain subsidy policies base on a household modelrdquo Journal ofChina Agricultural University vol 5 pp 171ndash178 2011

[17] L Ding X Wang Y Tan and C Kang ldquoThe optimal subsidyof cotton production in China-empirical analysis based on

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

principal component regression methodrdquo Journal of HuazhongAgricultural University vol 6 pp 5ndash9 2009

[18] M V P de Souza M Diallo R C Souza and T K N BaidyaldquoThe cost efficiency of the brazilian electricity distributionutilities a comparison of bayesian SFA and DEA modelsrdquoMathematical Problems in Engineering vol 2010 Article ID593059 20 pages 2010

[19] S Malmquist ldquoIndex numbers and indifference surfacesrdquo Tra-bajos de Estadistica vol 4 no 2 pp 209ndash242 1953

[20] D Caves L Christensen and W Diewert ldquoThe economictheory of index numbers and themeasurement of input outputand productivityrdquo Econometrica vol 50 no 6 pp 1393ndash14141982

[21] R Fare S Grosskopf M Norris and Zhongyang ZhangldquoProductivity growth technical progress and efficiency changein industrialized countriesrdquoAmerican Economic Review vol 84no 1 pp 66ndash83 1994

[22] R W Shepherd Theory of Cost and Production FunctionsPrinceton University Press Princeton NJ USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of