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INDEX NUMBERS

1. The employees of an American Company have presented the following data in support of theircontention that they are entitled to a wage adjustment. Dollar amounts shown represent the averageweekly take-home pay of the group :

Year 1983 1984 1985 1986

Pay 240 250 260 280Index 120 150 160 200(i) Compute the real wages.(ii) Compute the amount of pay needed in 1986 to provide buying power equal to that enjoyed in

1983.2. The price index of cosmetics was 110 in 1956 with base at 1950 and 120 in 1957 with 1956 as base. It

further increased by 30% in 1958 in relation to the price index of 1957 and decreased by 10% in 1959as compared to its level in 1958. What is the Chain base index number for 1959 with 1950 as base?

3. An index is at 100 in 1967. It rises 15% in 1968, falls 4% in 1969, falls 2% in 1970 and rises 10% in1971. Calculate the index for above 5 years with 1969 as base. What is the purchasing power of therupee in 1971 as compared to 1967?

4. Given the following data on weekly wages and consumer price index:Year 1968 1969 1970 1971 1972 1973Pay 109 112 116 125 135 138Index 113 118 127 138 144 150

(iii) In which year did the employees have the greatest buying power?(iv) What percentage increase in the weekly wages for the year 1973 is required (if any) to provide

the same buying power that the employees enjoyed in the year in which they had the highestreal wages?

5. What is meant by reversibility of an index number? Describe the time and factor reversal tests inthe theory of index numbers. Give a formula that satisfies both these tests.

6. The wholesale price index for the years 1952-1956 with 1948=100 is given below. Determine thewholesale purchasing power of the rupee in each of the given years in terms of 1954 rupee

Year 1952 1953 1954 1955 1956WPI (1948=100) 111.6 110.1 110.3 110.7 114.3

7. In 1990 the price of a commodity increased by 60% over that in 1980 while the production of thecommodity decreased by 30%. By what percentage did the total value of production of the commoditychange with respect to its value in 1980?

8. When will the Laspeyeres and Paasches price index numbers be equal? Show that the time reversaltest is satisfied by the Laspeyres and Paasches index numbers in a situation where the two indexnumbers are equal.

9. GNP rose from Rs.200 crores in 1970 to Rs.680 cr. in 1990. The consumer price index rose to 170 in1990, with 1970 as base. Population rose 60% over the period. Find the real per capita GNP index for1990 with 1970 as base.

10. Given below are two index number series. Splice them on the base 1974=100:Year 1970 1971 1972 1973 1974 1975

Old Price Index for steelBase 1965=100 141.5 163.7 158.2 156.8 157.1New Price IndexBase 1974=100 99.8 100.0 102.3

11. If the volume of sales of a firm increased by 20% while the relevant price index increased from 240 to270 over a certain period, compute the percentage rise in nominal value of sales.

12. Calculate the index of real wages for the following data with 1988 as base year:

Year 1988 1989 1990 1991 1992 1993Weekly wages(Rs) 109.5 112.2 116.4 125.8 135.4 138.1Consumer Price Index 112 119 127 138 143 150What should be the wages in 1993 so that purchasing power in 1993 is same as in 1988?

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13. The consumer price index for a group of workers was 250 in 1994 with 1980 as the base.(i) Compute the purchasing power of a rupee in 1994 compared to 1980.(ii) At what value of CPI would the purchasing power of a rupee e 25 paise?

14. The wholesale price index for the years 1952-1956 with 1948=100 is given below. Determine thewholesale purchasing power of the rupee in each of the given years in terms of 1954 rupee

Year 1952 1953 1954 1955 1956WPI (1948=100) 111.6 110.1 110.3 110.7 114.3

15. What are the consistency tests for index numbers? What requirement does each of these tests satisfy?Explain.

16. Labour and capital are used in two different proportions in products A and B, but the price of each inputis equal for both products. On the basis of the information given below, prepare, for the year 1980,separate price indices for labour and capital.

Product A Product BWeight for labour 60 70Weight for capital 40 30Cost of production index for 1980 ( Base yr 1970 ) 340 330

17. Combine the two series of index numbers given below to produce a new series with base 1996: Year 1992 1993 1994 1995 1996 1997 1998 1999 Old Series(1983=100) 225 270 300 New Series(1994=100) 100 110 120 140 170 200

18. Given the following data, compute the series of national income at current prices: Year 1985 1986 1987 1998

National Income at 1983 prices (Rs.billion) 200 220 240 250Price Index (1983=100) 120 125 130 132

19. Given below are the data for average wages in Rs. per hour for unskilled workers of a factory for theyears 1975-80 and the consumer price indices for these years. Determine the real wages of workers

and the purchasing power of the rupee in 1980 as compared to 1975. Year 1975 1976 1977 1978 1979 1980 C.P.I. (1975=100) 100 120.2 121.7 125.9 129.3 140

Average wage (Rs per hour) 1.2 1.9 2.2 2.3 2.4 3.1

20. From the following data prove that Fishers Index satisfies both Time Reversal and Factor Reversaltests:Commodity Base Year Current Year

Price Quantity Price Quantity A 6 50 10 60B 2 100 2 120C 4 60 6 60

21. From the data given in the following table, construct Laspeyres and Paasches price I Nos.Base Year Current Year

Commodity Price Expenditure Price ExpenditureA 2 40 5 75B 4 16 8 40C 1 10 2 24D 5 25 10 60

22. If the ratio between Laspeyres and Paasches index no. is 28:27, find the missing figures in thefollowing table:

Base Year Current Year Commodity Price(Rs.) Quantity(Kgs.) Price(Rs.) Quantity(Kgs.)

X 1 10 2 5Y 1 5 - 2

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23. The following are the index nos. of wholesale prices of a commodity based on the year 1996:Year : 1996 1997 1998 1999 2000 2001 2002Index No: 100 108 120 150 210 225 240Prepare new index numbers taking 1999 as base year.

24. The following table gives two index no. series. Splice them on the base 1999=100. By what percentagedid the price of the commodity rise between 1995 and 2000?

Year : 1995 1996 1997 1998 1999 2000Old I.No.(1990=100) : 141.5 163.7 158.2 156.8 157.1 --New I.No.(1999=100) : -- -- -- 99.8 100.0 102.3

25. The following table gives the annual income of a person and the general price index no. for the period1988 to 1996. Prepare the index no. of real income of the person. (Hint: prepare the series of realincome and then prepare the index no. of real income by taking real income of 1988=100)Year : 1988 1989 1990 1991 1992 1993 1994 1995 1996Income (Rs.000) : 36 42 50 55 60 64 68 72 75Price Index : 100 120 145 160 250 320 450 530 600

26. Prepare a spliced series of index nos with 1985 as base.

Years : 1980 1981 1982 1983 1984 1985 1986

Index A : 100 120 135 - - - -

Index B : - - 100 115 125 145 -

Index C : - - - - - 100 110

27. Show that Laspeyres Price Index can be written as a weighted average of price relatives. What are theweights?

28. The following data relate to the average weekly income of workers and the price index:Year : 1993 1994 1995 1996 1997 1998Weekly income (Rs.) : 800 819 825 876 920 924Price Index (1993=100) : 100 105 110 120 125 135

Calculate (i) Real income of workers of workers during the years 1993-1998(ii) Index numbers of real income with 1993 as base

29. Distinguish between fixed base and chain base methods of index number construction. When shouldthe latter be preferred?

30. From the following data on prices of commodities A, b and C calculate the chain base index numberswith 1999 as base:

Price in Rs.per unit

Commodity Year 1999 2000 2001 2002

A 4 6 8 10B 16 20 24 30C 8 10 16 20

31. Splice the following two price index number series with 1990 as base:Year : 1990 1991 1992 1993 1994 1995 1996 1997Series A : 100 120 125 150Series B : 100 110 120 95 105What is the purchasing power of the rupee for 1997 as compared to 1990?

32. The price relative (in %) and weights of three commodities are given below:Commodity Price Relative Weight

A 115 w1

B 125 w2

C 120 w1 + w2If the sum of wts is 20 and P Index no. for the commodities is 119, find the numerical value of weights.

33. Why is Fishers Ideal Index called Ideal?

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34 Given the following index nos. of wholesale prices of a commodity based on the year 1996, preparenew index numbers taking 1999 as base year.Year : 1996 1997 1998 1999 2000 2001 2002Index No: 100 108 120 150 210 225 240

35. The wholesale price index for the years 1952-1956 with 1948=100 is given below. Determine thewholesale purchasing power of the rupee in each of the given years in terms of 1954 rupee

Year 1952 1953 1954 1955 1956WPI (1948=100) 111.6 110.1 110.3 110.7 114.3

36. On the basis of figures of production of generators given below, construct:(i) Quantity index; (ii) Price Index (using 1990 as base)

Year 1190 1991 1992 1993 1994Units Produced (000) 24 30 32 38 44Value of Output(Rs.lakhs) 192 255 272 361 451

37. What are the objectives of constructing index numbers?

38. Discuss briefly the problems in the construction of Index numbers.

39. Show that if all prices increase by the same proportion, such that. p1i = p0i for all commodities wherei=1,2.n, then P01La = P01

Pa

40. Given the following data:

Year: 1995 1996 1997 1998 1999 2000 2001

Monthly Pay(Rs.): 10,500 11,000 11,500 12,500 13,500 14,000 14,500

Price Index: 115 120 130 138 144 150 160

(i) Calculate the real monthly pay for each year.

(ii) In which year did the employee have the highest purchasing power?

What percentage increase in the monthly pay for the year 2001 is required (if any) to compensate him

with the purchasing power in the year of his highest real pay?41. Using the following data show whether Laspeyres, Paasches and Fishers Price Index numbers satisfy

the Time Reversal and Factor Reversal tests.Commodity p0 q0 p1 q1

A 6 50 10 60B 2 100 2 120C 4 40 6 60

42. A department store sells stereo systems, TVs, and radios.. The percentage distribution of the totalsales volumes (in Rs.) is estimated as 30% stereos, 50% TVs and 20% radios. The prices of onestereo, one TV and one radio in 1990 wereRs.20,000, Rs.15,000 and Rs.500 respectively. Theirrespective prices in 1995 were Rs.25,000, Rs.20,000 and Rs.800. Compute the price index numberwith base 1990.

43. Calculate Laspeyres, Paasches and Fishers quantity and value index numbers.Base Year Current Year

Commodity Quantity(Kg) Price(RS./Kg) Quantity(Kg) Price(Rs./Kg)A 10.0 80 11.0 70B 8.0 85 9.0 90C 5.0 130 5.5 80

44. The consumer price index over a certain period increased from 120 to 215 and the wages of a workerincreased from Rs.1680 to Rs.3000. What is the gain or loss of the worker?