Ecological Economics 105 (2014) 139–153

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Ecological Economics

j ourna l homepage: www.e lsev ie r .com/ locate /eco lecon

Analysis

Linking common property resource management to humancapital outcomes

Ram Ranjan ⁎Dept. of Environment and Geography, Faculty of Science, Macquarie University, NSW 2109, Australia

⁎ Tel.: +61 2 98507989.E-mail address: ram.ranjan@mq.edu.au.

http://dx.doi.org/10.1016/j.ecolecon.2014.06.0050921-8009/© 2013 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 10 December 2013Received in revised form 1 May 2014Accepted 8 June 2014Available online xxxx

Keywords:Human capitalCommon pool resourcesClimate change, repeated droughts,social normsForestry managementOptimal forest harvestingSoil erosionSoil degradation

In regions where common pool resources provide significant support to their surrounding communities, any cli-mate change related shock could producemultiple livelihood repercussions. In this paper, a model explores howthe health of common pool resources could impact upon human capital outcomes for communities that struggleto find alternate livelihood options when traditional means such as agriculture become unsustainable. The man-agement of common pool resources is modeled as a strategic interaction process between two heterogeneouscommunities that are directly or indirectly dependent upon it. An unconstrained harvesting of common re-sources such as forestry not only depletes its stocks, but it also indirectly affects crop output through soil degra-dation. A number of situations are constructedwhere communities are able to successfully finance human capitalaccumulation through proper management of their common pool resources. However, results also warn thatcommunities that are faced with limited opportunities towards accumulating human capital must plan aheadto prevent the depletion of their common resources below critical levels. When non-linear feedbacks to soil deg-radation emanate from low levels of common pool stocks, human capital outcomes as well as future livelihoodsof such communities are threatened.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Common pool resources (CPRs) face the ‘tragedy of the commons’problem (Hardin, 1968). When adequately maintained, however, theycould provide additional support towards rural livelihoods. Marginalfarmers and landless labor types aremost directly affected by the deple-tion of CPRs as CPR based income comprises a higher proportion of theirconsumption. Then, there are agricultural farmers whomay not need torely directly on the CPRs but still benefit indirectly through the ecolog-ical services provided by CPRs. Dense forests can protect against soilerosion during heavy rainfall and flooding. Forests may also providefodder to support farmers' livestock, where livestock is often used as ahedging strategy to cope with prolonged droughts.

In the absence of property rights, social norms may endogenouslyevolve over how much CPRs to exploit and over the optimal mainte-nance of their stock, as has been argued in the literature (for instance,see Ostrom, 1990; Sethi and Somanathan, 1996). Ostrom (1996) laysout a number of circumstances where such social norms could evolvefor the betterment of forestry resources. Some of these conditions relateto low discount rates of users, higher importance of forests to their sur-vival, common interests, etc. Social normsmay evolve to punish the har-vesters or alternatively, those who do not contribute towards enforcing

norms could themselves be punished (see Sethi and Somanathan, 2006for a model incorporating the latter). The type of social norms that mayevolve towards the management of CPRs such as forests also dependsupon the level of heterogeneity amongst communities that are depen-dent upon it. For instance, Kant (2000) points out that landed house-holds with ruminants would depend upon the forests to sustain theirlivestock as well as to provide agricultural inputs such as composts,whereas landless and poor communities would be more concernedwith direct consumption of forest resources for their survival (also seePoteete and Ostrom, 2004).

In some societies government may step in to enforce harvestingrules. For instance, Copeland and Scott Taylor (2004) describe threetypes of CPR economies — namely ‘Hardin’, ‘Ostrom’ and ‘Clark’. Thisclassification ranks communities on their ability to sustainably managetheir common pool resources as a function of the price atwhich such re-sources are traded. Specifically, Hardin economies do not exhibit anycontrol over their resources even if the price of such resources becomesvery high, whereas Clark economies are very responsive to price chang-es in terms of their ability to manage resources efficiently (Copelandand Scott Taylor, 2004). Bray et al. (2006) provide examples fromMexico, where democratization of the forestry sector in the late 20thcentury led to the emergence of community forest economies (CFEs)whichwere conducive towards the generation of social and natural cap-itals in such environments. While, De Blas et al. (2011) provide an ex-ample of significant internal and external conflicts in Camerooniancommunity forests that have led to less than desired outcomes.

140 R. Ranjan / Ecological Economics 105 (2014) 139–153

Very often, the interests of those who directly benefit from CPRs arefound to be at loggerheadswith thosewho indirectly depend upon suchresources. For instance, landed farmers stand to lose from soil erosioncaused by uncontrolled flooding, the effect of which can be mitigatedthrough maintaining a dense forestry. Whereas, when faced withprolonged droughts and reduction in employment opportunities, land-less wage earners tend to intensify their reliance on CPRs as theirimmediate survival is at stake. In this particular context, an optimal ar-rangement would be where the landed farmers participate in plantingadditional trees, whereas the landless are required to reduce grazingintensity of their small ruminants and reduce reliance on forest prod-ucts for sustenance. However, differences in goals between differentuser groups often lead to conflicts and inequitable outcomes undersuch circumstances. Adhikari et al. (2004) provide evidence from com-mon forestry in Nepal pointing to the fact that poorer households havereduced access to forestry products whereas well-off households areable to appropriate a larger share of the same. Pradhan and Patra(2013) also find evidence relating to higher difficulties encountered injoin forestry management when communities differ in their socio-economic conditions.

Climate change could add to the mix of the above challenges by re-ducing forest cover and changing the composition of species within.The economic consequences of such changes have been estimated tobe immense globally (see Hanewinkel et al., 2013; Thuoller et al.,2011). Climate change could lead to forest dieback, which will notonly provide feedback carbon emissions to the atmosphere, but alsochange the nature of the soils (Peterman and Bachelet, 2012). The im-pact of climate change on forests in Asia has been particularly predictedto be high (Somaratne and Dhanapala, 1996; Zhao et al., 2005). Forestdegradation in the Asia Pacific region has already contributed to lowsoil quality thereby reducing its ability to provide high quality orquantity crop yields (FAO, 1999). Furthermore, by reducing the carryingcapacity of the CPRs, climate change will exacerbate the existing con-flicts over CPR usage norms. Climate change would also reduce agricul-tural output and hence the demand for landless labor, thereby resultingin intensification of their reliance upon the CPRs.

In this paper, we explore another aspect of CPR management chal-lenges, which has not been touched upon in the literature thus far.This concerns exploring the linkages between human capital and CPRstocks and how the maintenance or depletion of the latter could affectfuture human capital outcomes in small scale societies. The key questionthat is being posed in this paper is how those rural economies, whichare struggling to transition out of sustenance based livelihoods throughinvestment in human capital, will be affected by climate change relatedshocks to the CPRs? Further, how do social norms evolve under climatechange related stress and what are the conditions under which suchsuccessful transitions may not materialize? These questions are ad-dressed in the context of common pool resources in Asian economies.

Following Becker's seminal work on human capital (see Becker,1964), a vast body of literature has emerged linking human capital out-comes to growth at national levels as well as associating it with differ-ences in wages and national incomes of various countries. Humancapital in the context of rural areas has been studied by Huffman(2001) and Taylor and Martin (2001). The roles of different types of in-stitutions in different societies have also been explored recently byAcemoglu and Dell (2010) with respect to their impact on makingschooling accessible and cheaper. However, how human capital out-comes are affected amongst CPR based communities, especially whenclimate change threatens the sustainability of such CPRs, is a questionthat has remained unexplored thus far.

In order to take up and address these important questions, a dynam-ic optimization model is developed that links crop output to the healthof the CPRs. One community (the landed farmers) invests in humancapital augmentation of their children and hence needs to have profit-able agriculture to finance such human capital investments. The othercommunity (the landless group) directly relies upon the CPR for their

sustenance. Both crop output and the CPRs are faced with the risk ofclimate change related shocks materializing in the future. Social normsendogenously evolve within this heterogeneous community over man-agement of the CPR, as CPR depletion can indirectly and adversely affectcrop output.

The literature addressing the evolution of social norms and capitalsupports this endogeneity assumption. For instance, Krishna (1994)provides an example from South India where social norms and socialcapital endogenously evolve with increasing resource scarcity. Watersupply uncertainty promotes betterwatermanagement through forma-tion of collectives (that self-impose sustainable water use practices)whereas regions with relatively less water scarcity see no such endoge-nous institutional formations (Krishna, 1994). Group size also affectsthe successful enforcement of rules for governing CPRs, as smallergroups are found to bemore effective towards harnessing collective ac-tion compared to larger groups. In smaller groups, the tendency to freeride is absent, whereas in the case of larger groups, collective action canbe enforced only through punishments and coercion (Olson, 1965). Inthe context of joint forestry management, Ostrom (1996) argues thatgroup heterogeneity can lead to differences in interests of the usersand therefore agreeing upon and enforcing a common set of rules canbe difficult and costly.

The next section provides the model outline. A formal dynamicoptimization model is presented following the model outline. Resultsare derived through a numerical example. The paper concludes bydiscussing some of the insights that emerge through the modeling ofthe complex inter-linkages between climate change related threats tothe sustainability of CPRs as well as the livelihoods and human capitaloutcomes of the communities that are directly and indirectly dependentupon it.

2. Model Outline

Themodel presented in this paper draws from cases of several farm-ing districts in South India (in particular from Anantapur, see Conroy,2001 for a background) where farming and forestry based communitieshave co-existed historically and were well supported by the surround-ing common pool forestry resources. However, over time, as repeateddroughts have made water scarce, it has affected the crop outputs ofthe landed communities. This has also adversely affected the demandfor casual labor that was earlier supplied by the landless communities.When facedwith reduced employment opportunities, the landless com-munities have increased their reliance upon common pool resources forsustenance thereby leading to its rapid depletion. This in turn has led torapid soil erosion (from uncontrolled runoffs) and set off further feed-back effects through significantly reducing crop outputs and demandfor casual labor. This necessitated the need for stricter forestrymanage-ment in order to prevent further soil erosion and improve the livelihoodof the communities. There are examples from elsewhere of similarproblems arising due to excessive forest degradation. Forestry is mostlyrelied upon by rural households for fuel wood consumption and live-stock grazing in Kenya (Muchena et al., 2005). This has led to unsustain-able rates of deforestation. In general, as result of deforestation, the rateof soil degradation in developing countries of Central America, Asia andAfrica has been very high (Scherr, 1999).

In this section, we develop a modeling framework that incorporatessome of the key challenges faced by two heterogeneous communitiesrelying upon a CPR. Consider that there are two types of farmers, thelanded and the landless categories. Additionally, assume that there areonly two farmers, each representing their respective communities.The landed farmer grows a composite crop and the derived income isused to finance consumption and educational expenses of their chil-dren. The landless farmer relies upon the CPR for their livelihood suste-nance such as through collecting fuel wood and grazing of smallruminants in the common lands.

141R. Ranjan / Ecological Economics 105 (2014) 139–153

Wewish to explore how human capital investment decisions are af-fected by various factors including CPR health, and concentrate only onthe landed type farmer with respect to schooling decisions. The child ofthe landless farmer is assumed to be assisting the family in generatingsustenance income through harvesting forestry products and does notgo to school. Schooling is subsidized and incentive programs, such asmid-daymeals, exist to prevent school dropouts. While there are no di-rect costs of schooling, there are indirect opportunity costs of schoolingtime for the children of the landed farmer. For the landed farmer, theopportunity cost is the reduced output in agriculture, whereas for thelandless farmer, if their childrenwent to school, it would be the reducedCPR based income. Investment in education yields rewards by providingassured employment outside of agriculture. In reality, farmers may notencourage schooling of their children if employment after completionof schooling is not assured. Here we assume that while education willlead to some form of employment after schooling, there is a thresholdlevel of education that needs to be crossed before the wages becomesignificant.

Next, introduce the evolution of social norms related to CPR harvest-ing. The amount of CPR harvesting per time period is a function of socialnorms in the society which comprises these two categories of farmers.Further, it is assumed that it is only the landless type that is reliantupon the CPR for their sustenance and that the landed group does notdirectly access the CPR. While social norms and its dynamics has beenawidely researched topic, it is still a gray area. Social norms could be en-dogenous to the conflicting financial and non-financial interests of var-ious factions in the society. The dynamics of social norms in the presentcontext are affected by the ability of groups to successfully enforce a setof regulations to manage the CPR. In the absence of effective regulation,social norms could dissipate leading to depletion of the CPR. Here wemake the evolution of social norms endogenous to human capital accu-mulation objectives of the landed farmer. When CPR health is essentialfor ensuring steady source of revenues, social norms will evolve to pro-tect CPR. However, when different groups rely differentially upon theCPR and are affected in varying degrees by its depletion, social normdynamics may not be linear and could exhibit path dependence orhysteresis.

In our particularmodel, the landed farmer needs to conserve CPRs toavoid loss in agricultural productivity from soil erosion from uncon-trolled flooding in the absence of dense forestry. The cost of educationof the landed farmer's child can be financed through agricultural incomeand the farmer is only indirectly dependent upon CPRs. That is, the land-ed farmer has an income buffer. The landless labor relies more inten-sively and directly on CPRs and has no such buffer. The landed farmeris assumed to be the dominant of the two types (owing to higherwealthand caste based status) and dictates the norms with respect to harvest-ing. If the landless type does not harvest as dictated, they suffer a cost.The cost of harvesting CPRs, therefore, comprises the direct cost ofsearching for and harvesting forestry products as well as the costsimposed by the landed farmer for harvesting the CPR. The landedfarmer accomplishes this punishment enforcement indirectly throughinvesting in accumulation and maintenance of social norms whichmust be obeyed by the CPR harvesters. Since, time spent in accumulat-ing norms is time lost in farming, the landed farmer suffers aswellwhiletrying tomaintain CPRhealth.We formalize the above outline through adynamic optimization framework next.

3. A Model of CPR Health and Human Capital Outcomes

Consider that a small scale economy owns natural resources, thestock of which is given by x(t), which are mainly in the form of a forestecosystem. The rate of growth of this CPR stock is given as:

x tð Þ ¼ ρ � x tð Þ � 1− x tð Þk

� �−h tð Þ; ð1Þ

where ρ is the intrinsic growth rate of CPR, h(t) is the annual harvestrate of CPR and k is its maximum carrying capacity. The landed farmerwho depends upon farming for their main source of subsistence incomefaces the following crop production function, q(t), with respect to soilquality, s(t), labor input, l(t), and water, w(t):

q tð Þ ¼ s tð Þ � l tð Þ � ηw � w tð Þα0

w tð Þα0 þ α1

� �; ð2Þ

where α0 and α1 are the parameters that lead to a non-linear relationbetween water applied and crop output, and ηw is the maximum cropoutput that could be produced when applying any amount of wateron one unit of land using one unit of labor and when the soil quality isone unit as well.

The landed farmer also spends a part of their time enforcing socialnorms, N(t), with respect to harvesting in the CPR. Assuming that theyhave one unit of total time available per year, the time left for enforcingnorms would be 1 − l(t).

Soil quality degrades with the depletion of the CPR stock. The soilquality dynamics is modeled as:

s tð Þ ¼ srenew−ηs �k−x tð Þð Þφ0

k−x tð Þð Þφ0 þ φ1; ð3Þ

where srenew is the natural rate of annual soil replenishment and the

term ηs � k−x tð Þð Þφ0k−x tð Þð Þφ0þφ1

represents a non-linear rate of decline in soil qual-

ity with CPR stock depletion. Soil regeneration rate is usually very slow,at about 0.025 mm to 0.125mmper year, and is highly variable (Parikhand James, 2012). The decline in soil quality becomes muchmore rapidand increases non-linearly as the difference between themaximumcar-rying capacity and the current CPR stock level increases. Parameters φ0

andφ1 determine the sensitivity of this relationship between the differ-ence in the maximum carrying capacity and current CPR stock and therate of annual soil erosion. A higher value of φ1 implies that a muchhigher difference would be needed to make a sharp upward jump insoil loss rate (so high φ1 signifies more resilient soil), whereas a highervalue of φ0 would imply a much steeper increase in the rate of soil deg-radation as this difference increases (so a high φ0 would signify low soilresilience).

When the stock of CPR is depleted beyond a certain threshold (cap-tured by the degree of separation of the current stock from the carryingcapacity of the CPR), there is a significant increase in soil erosion rateleading to a complete loss in agricultural productivity. For instance,when CPR is totally depleted, soil quality erodes at a maximum annualrate of, srenew−ηs � kφ0

kφ0þφ1, which can be further written as srenew − ηs

when k is large. Whereas, when the current stock of CPR is at itsmaximum sustainable level of k, the soil quality is augmented annuallyat srenew. We further assume that srenew≪ ηs, so that under complete de-pletion of the CPR stock, soil erosion is very high.

The financial wealth dynamics,mtð Þ, for the landed farmer is given as:

m tð Þ ¼ π � q tð Þ−c el tð Þð Þ þ 1−el tð Þð Þ � i tð Þ−c tð Þ; ð4Þ

wherem(t) is the stock of accumulatedwealth, π is the fixed price of thecomposite agricultural crop, c(el) is the annual cost of acquiring educa-tion as a function of the educational effort el(t), and (1− el(t)) ⋅ i(t) isthe wage income earned by the landed farmer's child. Annual wagesare defined as i(t) and are a function of the accumulated stock of educa-tion, E(t), which evolves according to the equation:

E tð Þ ¼ f e tð Þð Þ−δ � E tð Þ; ð5Þ

where the term δ ∙ E(t) reflects the fact that acquired human capital (orthe stock of education) could be lost gradually if not continually aug-mented. The variable f(e(t)) is the annual rate of transformation of edu-cational effort into stock of human capital E(t).

142 R. Ranjan / Ecological Economics 105 (2014) 139–153

Wages evolve non-linearly with human capital, so that a thresholdlevel of human capital must be crossed before wage earnings becomesubstantial. This relationship between wages and human capital isgiven as:

i tð Þ ¼ ηh �E tð Þχ0

E tð Þχ0 þ χ1; ð6Þ

where χ0 and χ1 are the parameters that determine the minimumhuman capital needed before its impact on wages could becomesignificant. Also, ηh is the maximum possible wage that a farmer'schild is projected to earn for any level of human capital acquired. Pa-rameter ηh itself could increase over time, but here we avoid thiscomplication.

The landed farmer maximizes utility, U(t), from consumption, c(t),which takes a logarithmic form to reflect risk aversion:

U tð Þ ¼ log c tð Þð Þ: ð7Þ

Next, we derive the CPR harvesting rules. The time spent by thelanded farmer in enforcing social norms has implications for the har-vesting of the CPR by the landless wage earning household. The CPR isprimarily relied upon by the landless type farmer for meeting theirsustenance needs. Let us assume that the CPR is in a mildly degradedstate which makes harvesting for meeting sustenance needs costly.There is an additional cost associated with harvesting, which comesin terms of the social norms being enforced by the landed farmer.The landless farmer derives non-linear benefits, log(h(t)), from theCPR, where the cost of harvesting is non-linear in harvesting effortas well as in the stock of social norms, N(t), the dynamics of whichis given as:

N tð Þ ¼ v 1−l tð Þð Þ þ ηn �N tð Þγ0

N tð Þγ0 þ γ1−δN � N tð Þ: ð8Þ

In Eq. (8), v(1 − l(t)) is a function relating time spent enforcingnorms into its effect on the accumulation of stock of norms and δN isthe annual decay in norms, which implies that norms need to be con-stantly enforced to keep their stock constant. The term, ηn � N tð Þγ0

N tð Þγ0þγ1,

provides a positive feedback boost to social norms once they havebeen accumulated beyond a certain level and parameters γ0 and γ1 de-termine the level of stock at which this feedback effect becomessignificant.

The cost of CPR harvesting, c(h(t), N(t)), is multiplicative in harvest-ing and the stock of social norms established by the landed community,which tries to prevent any harvesting to avoid further forestry and soildegradation, and is given as:

c h tð Þ;N tð Þð Þ ¼ β0 � h tð Þβ1 � N tð Þϕ1 ; ð9Þ

where β0 and β1 are the parameters determining non-linear harvestingcosts andϕ1 is the effectiveness of social norms in imposing punishmentfor a given level of harvesting. The above form of the cost function alsoimplies thatwhen social norms are non-existent therewould be no har-vesting costs incurred. This form has additional implications that whenthe landless farmer harvests too much, a higher social normwill lead tohigher punishment compared to when the norms are lower.

The landless farmer simply optimizes their utility from per periodconsumption and acts as a myopic agent in the sense that they do notplan for the future. Another way to put this is that they exhibit hightime discounting given their poor livelihood status. Their first order op-timization condition with respect to harvesting choice leads to:

β0 � β1 � h tð Þβ1−1 � N tð Þϕ1 ¼ 1h tð Þ ; ð10Þ

which upon further simplification yields harvesting effort as a decliningfunction of the stock of social norms:

h tð Þ ¼ N tð Þ−ϕ1

β0 � β1

( ) 1β1

: ð11Þ

The landed farmer can incorporate this relationship in their optimi-zation problem with respect to human capital, social norm and wealthaccumulation. The current value Hamiltonian problem for the landedfarmer is written as:

log c tð Þð Þ þ μ1 tð Þ � π � s � l tð Þð Þ � ηw � w tð Þαw tð Þα þ α0

� �� �−c el tð Þð Þ þ 1−elð Þ � i tð Þ−c tð Þ

� �

þμ2 tð Þ � f e tð Þð Þ−δ � E tð Þf g þ μ3 tð Þ � v 1−l tð Þð Þ þ ηn �N tð Þγ0

N tð Þγ0 þ γ1−δN � N tð Þ

� �

þμ4 tð Þ � ρ � x tð Þ � 1− x tð Þk

� �− N tð Þ−ϕ1

β0 � β1

( ) 1β1

8<:

9=;þ μ5 tð Þ

� srenew−ηs �k−x tð Þð Þφ0

k−x tð Þð Þφ0 þ φ1

� �; ð12Þ

where μ1(t), μ2(t), μ3(t), μ4(t) and μ5(t) are the shadow prices of stocksof financial wealth, human capital, social norm, CPR and soil quality re-spectively. First order condition with respect to consumption decisiongives:

1c tð Þ ¼ μ1 tð Þ: ð13Þ

Eq. (13) simply requires that marginal utility from consumption beequated to the shadow price of financial wealth along an optimalpath. However, since financial wealth is needed for both consumptionas well as human capital accumulation, and is affected by decisionswith respect to social norm and soil quality preservation, consumptiondecisions will also be tied to the same constraints. First order conditionwith respect to agricultural labor time allocation by the farmer yields:

μ1 tð Þ � π � s tð Þ � ηw � w tð Þαw tð Þα þ α0

� �� �¼ μ3 tð Þ � v0 1−l tð Þð Þ: ð14Þ

The shadow prices of stock of financial wealth and that of the stockof social norms are inter-linked by the above condition. A marginalinput of labor put into farming enhances crop output, but it also affectsthe stock of social norms as the time spent in farming is time lost notaugmenting social norms. The marginal productivity of labor inagriculture is a function of soil quality and water. So, at lower wateravailability or lower soil quality, the marginal productivity of labor inagriculture will be lower. This will affect the tradeoff derived in theabove equation — that between crop income and social norm augmen-tation. First order condition with respect to educational effort of thechild yields:

μ1 tð Þ � c0 el tð Þð Þ þ i tð Þ� � ¼ μ2 tð Þ � f 0 e tð Þð Þ: ð15Þ

The farmer's child's level of educational effort ties the shadow pricesof financial wealth to that of stock of human capital. Earlier we saw thatshadow price of wealth was related to that of social norms, therebymaking the shadow prices of stocks of human capital and social normsinterlinked. This inter-linkage could again turn out to be complex topredict as the dynamics of both social norm as well as human capitalare assumed non-linear. Human capital needs to be augmented contin-uously given its depreciation ratewhich increases in the stock of humancapital. When human capital based wages are higher, the shadow priceof human capital will be higher, therefore requiring higher current con-sumption sacrifices and use of financial wealth towards educational ex-penses. This creates a tradeoff between current income generationactivities to finance education andmaintaining future sources of income

143R. Ranjan / Ecological Economics 105 (2014) 139–153

through wage income as well as crop income. Investment in socialnorms ensures that crop income does not decline in the future; howev-er, if future crop income is expected to be lower than the future wageincome, investment in social norms could be discounted. There are anumber of scenarios where social norm investment could take a backseat. First, when the financial wealth level of farmers seeking humancapital is higher, whichmitigates the reduction in crop income to a cer-tain extent allowing thema buffer timeperiodwithinwhich to augmentskills and become employable outside of agriculture. Second, future cli-mate change relatedwater scarcity could reduce the carrying capacity ofthe CPRs, thereby indirectly threatening reduced crop income throughlower soil quality and also directly affecting crop productivity throughlower rainfall. When faced with such a possibility, the incentive to in-vest in CPR augmentation through social norms or even through directinvestments may be absent. This is evident from looking at the no-arbitrage condition over the shadow price of stock of CPR, which yields:

μ 4 tð Þ ¼ − ddx tð Þ μ4 tð Þ � ρ � x tð Þ � 1− x tð Þ

k

� �� �þ μ5 tð Þ � −ηs �

k−x tð Þð Þφ0

k−x tð Þð Þφ0 þ φ1

� �� �þr � μ4 tð Þ: ð16Þ

Shadow price of stock of CPR is a function of its own stock, as a rela-tively higher stock leads to higher growth, as well as it is affected by theshadow price of stock of soil quality. The latter leads to lower crop in-come at lower soil quality stock thereby also reducing the shadowprice of the CPR stock. No-arbitrage condition with respect to the shad-ow price of stock of social norms yields:

μ 3 tð Þ ¼ − ddN tð Þ μ3 tð Þ � ηn �

N tð Þγ0

N tð Þγ0 þ γ1−δN � N tð Þ

� �þ μ4 � − N tð Þ−ϕ1

β0 � β1

( ) 1β1

8<:

9=;

8<:

9=;

þr � μ3 tð Þ: ð17Þ

Further, the no-arbitrage condition with respect to the stock of soilquality yields:

μ 5 tð Þ ¼ − dds tð Þ μ1 � π � s tð Þ � l tð Þð Þ � ηw � w tð Þα

w tð Þα þ α0

� �� �þ r � μ5 tð Þ:

�ð18Þ

Let us briefly explore the steady state condition for the stock of CPR.In the steady state we can write:

x tð Þ ¼ ρ � x tð Þ � 1− x tð Þk

� �− N tð Þ−ϕ1

β0 � β1

( ) 1β1

¼ 0; ð19Þ

and also from Eq. (8), we get:

N tð Þ ¼ v 1−l tð Þð Þ þ ηn �N tð Þγ0

N tð Þγ0 þ γ1−δN � N tð Þ ¼ 0: ð20Þ

Eqs. (19) and (20) can be further simplified to:

ρ � x tð Þ � 1− x tð Þk

� �¼ N tð Þ−ϕ1

β0 � β1

( ) 1β1

; and ð21Þ

v 1−l tð Þð Þ þ ηn �N tð Þγ0

N tð Þγ0 þ γ1¼ δN � N tð Þ; ð22Þ

which gives a relationship between the steady state stocks of naturalcapital and social norms as:

N tð Þ ¼ β0 � β1 � ρ � x tð Þ � 1− x tð Þk

� �� �β1� �− 1

ϕ1: ð23Þ

If we re-define social norm enforcement effort (1− l(t)) as n(t), onecan also derive a steady state relationship between the stock of CPR andthe optimal social norm enforcement effort as:

v n tð Þð Þ ¼ δ � N tð Þ−ηn �N tð Þγ0

N tð Þγ0 þ γ1¼ δ � β0 � β1 � ρ � x tð Þ � 1− x tð Þ

k

� �� �β1� �− 1

ϕ1

−ηn �β0 � β1 � ρ � x tð Þ � 1− x tð Þ

k

� n oβ1n o−γ0

ϕ1

β0 � β1 � ρ � x tð Þ � 1− x tð Þk

� n oβ1n o−γ0

ϕ1 þ γ1

:

ð24Þ

4. CPR and Human Capital Outcomes under Climate Change Risk

Now consider that there exists a risk of climate change related shockto the CPR in the near future. This risk is exogenous in that the localfarmers are unable to mitigate it. Further assume that the hazard rateof this climate event,λ tð Þ, follows an exponential distribution (for similarrisk formulation, see Clarke and Reed, 1994; Feinerman and Tsur, 2014;Tsur and Zemel, 1995). The climate change related shock could arrive intwo forms, one through reduced rainfall, or two, through directly andabruptly reducing the carrying capacity of the CPR. One may even as-sume that both these possibilities are likely to occur simultaneously orcould be inter-related. For simplicity, let us first begin with only therisk of a reduced carrying capacity being present in the near future.

In the post-climate event scenario, the stock dynamics of the CPRwill be given as:

x tð Þ ¼ ρ � x tð Þ � 1− x tð Þkpost

!−h tð Þ; ð25Þ

where kpost is the reduced carrying capacity of the CPR. After this event,the landed farmer faces the same optimization problem as before, butnow with a reduced carrying capacity of the CPR. Let Vpost(x(t), s(t),m(t), E(t)) be the value function obtained after making optimal choiceswith respect to labor, education, consumption and social norm invest-ment decisions in the post-climate change scenario where the CPR car-rying capacity has been adversely affected. To solve for this valuefunction, the utility levels obtained after optimizing over the controlchoices need to be calibrated for each possible combination of thestock variables that remain at the beginning of the post-event optimiza-tion problem. This value function, once solved for, can then be insertedinto the following optimization problem, which is to maximize:

∫∞

0

log c tð Þð Þ � exp −r � tð Þ � exp −λ tð Þð Þ þ λ tð Þ � exp −λ tð Þð Þ

� exp −r � tð Þ � V x tð Þ; s tð Þ;m tð Þ; E tð Þð Þ dt;ð ð26Þ

subject to the previously defined equations of motions for all stock var-iables. Note that since V(x(t), s(t), m(t), E(t)) already incorporates thereduced carrying capacity, Eq. (26) uses the original carrying capac-ity of the CPR in the CPR stock dynamic equation. This is becauseEq. (26) is maximizing optimal decisions where the expected utili-ties before and after the climate change event are separately incorpo-

rated. Specifically, the term ∫∞

0log c tð Þð Þ � exp −r � tð Þ � exp −λ tð Þð Þd t,

maximizes utility until the climate change event arrives and the term

∫∞

0

λ tð Þ � exp −λ tð Þð Þ � exp −r � tð Þ � V x tð Þ; s tð Þ;m tð Þ; E tð Þð Þdtð , maximizes

utility outcomes in the post-event time periods. Eq. (26) represents asimplified form of the overall optimization problem (refer to Clarkeand Reed, 1994 for setting up of optimization problems involving

144 R. Ranjan / Ecological Economics 105 (2014) 139–153

similar hazard functions). The current value Hamiltonian (cvh) in thepresence of climate risks is written as:

log c tð Þð Þ tð ÞÞ � exp −r � tð Þ � exp −λ tð Þð Þ þλ tð Þ � exp −λ tð Þð Þ � exp −r � tð Þ

�ðV x tð Þ; s tð Þ;m tð Þ; E tð Þð Þ þ μ1 tð Þ �(π � ðs tð Þ � l tð Þð Þ

� ηw � w tð Þαw tð Þα þ α0

� �−c el tð Þð Þ þ 1−el tð Þð Þ � i tð Þ−c tð Þ

)

þμ2 tð Þ � f e tð Þð Þ−δ � E tð Þf g þ μ3 tð Þ

� v 1−l tð Þð Þ þ ηn �N tð Þγ0

N tð Þγ0 þ γ1−δN � N tð Þ

� �þ μ4 tð Þ

� ρ � x tð Þ � 1− x tð Þk

� �− N tð Þ−ϕ1

β0 � β1

( ) 1β1

8<:

9=;þ μ5 tð Þ

� srenew−ηs �k−x tð Þð Þφ0

k−x tð Þð Þφ0 þ φ1

� �þ μ6 tð Þ �λ tð Þ;

ð27Þ

where μ6(t) is the shadow price of the stock of the cumulative hazardfunction. Deriving the no-arbitrage condition over the shadow price ofstock of CPR leads to:

μ4 tð Þ ¼ − ddx tð Þfλ tð Þ � exp −λ tð Þð Þ � exp −r � tð Þ � ðV 0

x x tð Þ; s tð Þ;m tð Þ; E tð Þð Þ

þμ4 tð Þ � ρ � x tð Þ � 1− x tð Þk

� �� �þ μ5 � −ηs �

k−x tð Þð Þφ0

k−x tð Þð Þφ0 þ φ1

� �gþr � μ4 tð Þ: ð28Þ

Compared to the no-risk case, now thedynamics of the shadowpriceof stock of CPR incorporates the effect a marginal change in its ownstock has on the post-climate value function. If climate change event

0

0.5

1

1.5

2

2.5

3

1 3 5 7 9 11 13 15 17 19 21 23 25

Harv

est(

Thou

sand

Tonn

es/Y

ear)

T

base case phi1=.5

x0=100 s0=75

chi1=50 v=.5

Fig. 1. Time paths of CPR harve

arrives at a time when the current stock of CPR is low, it will adverselyaffect the post-event value function as it may no longer be optimal totry to invest effort towards preserving the CPR through social norm re-inforcement. A farmermay be better off spending all their time farmingand augmenting their human capital at a quicker rate. On the otherhand, if the climate change event mainly affects the future rainfall pat-terns and leaves the carrying capacity un-altered, the shadow price ofstock of CPR will be mostly influenced by the last term in Eq. (28)

under brackets, μ5 � −ηs � k−x tð Þð Þφ0k−x tð Þð Þφ0þφ1

n o, which is the shadow price of

the stock of soil quality. Low rainfall adversely affects the crop outputwhereas a better soil quality augments it, so a reduction in rainfallcould be balanced by a higher CPR investment as along as the marginalcosts of labor time dedicated to increasing soil productivity through so-cial norm augmentation are not exceeded by the direct marginal pro-ductivity of labor in agriculture. We take recourse to a numericalexample to further explore and illustrate these tradeoffs.

5. A Numerical Example

The intrinsic growth rate of the forest ecosystem is assumed to be0.1. At this rate, when the initial stock of forestry is 10% of its maximumcarrying capacity of 100 (thousand tons), it takes roughly 25 years toreach half the carrying capacity andwhen the initial stock is half the car-rying capacity at 50, it takes 25 years to reach about 90%of itsmaximumcarrying capacity. The value for the annual rate of soil regeneration ischosen at 0.025 mm per year. Annual rainfall is randomly generated inGAMS using a mean of 400 mm and a standard deviation of 100 mm.The farmer, however, is aware of this pattern of rainfall and hence rain-fall is not stochastic for the farmer.

The maximum total time available to the farmer for allocating to-wards farming and social norm accumulation is 1 unit per year. Thefarmer's child also has one unit of time per year which is allocated

27 29 31 33 35 37 39 41 43 45 47 49 51ime

phi1=.9 x0=50

s0=30 m0=400

v=.25 low rain

sting under all scenarios.

0

1

2

3

4

5

6

7

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Stoc

kof

Soci

alN

orm

s

Time

base case phi1=.5 phi1=.9 x0=50

x0=100 s0=75 s0=30 m0=400

chi1=50 chi1=45 v=.5 v=.25

low rain

Fig. 2. Time paths of accumulated social norms under all scenarios.

145R. Ranjan / Ecological Economics 105 (2014) 139–153

between working and human capital accumulation.We further assumethat the farmer's child can invest up to a maximum of half of their timeeach year in acquiring human capital and the remaining in earningwages from that human capital. That is, if the child chooses to workmore than half the available time per year they can do so, this however,

0

20

40

60

80

100

120

1 3 5 7 9 11 13 15 17 19 21 23 25

CPR

Stoc

k(T

hous

and

Tonn

es)

T

base case phi1=.5

x0=100 s0=75

chi1=50 chi1=45

low rainfall

Fig. 3. Time paths of stocks of CPR ob

will reduce the time available towards education. The equation for CPRstock dynamics is given as:

x tð Þ ¼ 0:1 � x tð Þ � 1− x tð Þ100

� �−h tð Þ; x0 ¼ 75: ð29Þ

27 29 31 33 35 37 39 41 43 45 47 49 51ime

phi1=.9 x0=50

s0=30 m0=400

v=.5 v=.25

tained under various scenarios.

146 R. Ranjan / Ecological Economics 105 (2014) 139–153

Price of the agricultural crop is assumed to be 20 rupees per kilo.Crop output is measured in tons per hectare with the representativefarmer having one hectare of land. The modified crop production func-tion can be specified as:

q tð Þ ¼ 10 � s tð Þ100

� l tð Þ �w tð Þ80

3

w tð Þ80

3 þ 20

!; ð30Þ

and 80 is a parameter value that converts rainfall into its effect on cropyield. Eqs. (31)–(36) present the rest of the equationswith base case pa-rameter values assigned to them as:

s tð Þ ¼ 0:025− 0:1 � 100−x tð Þð Þð Þ30:1 � 100−x tð Þð Þð Þ3 þ 10

; s0 ¼ 40: ð31Þ

In Eq. (31), the starting value of soil quality is assumed to be 40units with an annual regeneration capacity of 0.025 units. A reduc-tion in CPR stock from its maximum carrying capacity increases soilerosion. Human capital declines in proportion to its stock as givenby Eq. (32):

E tð Þ ¼ e tð Þ−0:1 � E tð Þ: ð32Þ

0

10

20

30

40

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19 21 23 25

Soil

Qua

lity

T

base case phi1=.5

x0=100 s0=75

chi1=50 v=.5

Fig. 4. Time paths of soil qualit

Maximumwages based upon human capital are assumed to be 600thousand rupees per year and wages increase non-linearly in humancapital as:

i tð Þ ¼ m0 �E tð Þ2

E tð Þ2 þ 40;m0 ¼ 600: ð33Þ

Social norm dynamics are written as:

N tð Þ ¼ 1−l tð Þð Þ � 1þ 1 � N tð Þ2N tð Þ2 þ 20

−0:1 � N tð Þ; v ¼ 1; ηn ¼ 1; ð34Þ

and the cost of harvesting (in thousand rupees per ton) as a function ofsocial norms is specified as:

c h tð Þð Þ ¼ 0:2 � h tð Þ2 � N tð Þ0:75: ð35Þ

The calibration of parameters governing the rate of harvesting of CPRis done so that when the value of ϕ1 is 0.75 and if the farmer were tospend all their time in enforcing social norms (which have a startingvalue of 1) instead of farming, the CPR harvesting would reduce tohalf its initial level (of 1.58) in about seven years' time. When ϕ1 ishigher at 1, it takes only four years to reduce harvest by half from itsstarting level of 1.58. At ϕ1 equals 1.5, harvesting is reduced to 0.47 in5 years' time when all of labor time is spent enforcing social norms.

27 29 31 33 35 37 39 41 43 45 47 49 51ime

phi1=.9 x0=50

s0=30 m0=400

v=.25 low rainfall

y under various scenarios.

-0.4

0.1

0.6

1.1

1.6

2.1

2.6

3.1

3.6

4.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Hum

anCa

pita

l

Time

base case phi1=.5 phi1=.9

x0=50 x0=100 s0=75

s0=30 m0=400 chi1=50

v=.5 v=.25 low rainfall

Fig. 5. Time paths of human capital accumulated under various scenarios.

0

1

2

3

4

5

6

7

8

9

10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Crop

Out

put(

Tonn

es/H

ecta

re)

Time

base case phi1=.5 phi1=.9 x0=50 x0=100

s0=75 s0=30 m0=400 chi1=50 chi1=45

v=.5 v=.25 low rainfall

Fig. 6. Time paths of crop output generated under various scenarios.

147R. Ranjan / Ecological Economics 105 (2014) 139–153

148 R. Ranjan / Ecological Economics 105 (2014) 139–153

The base case value ofϕ1 is chosen to be 0.75. Following this, the optimalharvesting effort (in thousand tons) for the landless farmer is given as:

h tð Þ ¼ N tð Þ−0:75

0:2 � 2

( )12

: ð36Þ

We first run themodelwithout the risk of any climate change. In thebase case, the harvesting outcomes are depicted in Fig. 1. In Fig. 1 wealso consider several scenarios that vary key parameters (one at atime) to assess how harvesting and other outcomes change. Since har-vesting can only be indirectly influenced through social norms, we seeincreasing harvesting trends for certain periods and then a steep declinebefore the pattern repeats itself. The gradual increase in harvesting overtimeoccurs due to declining social norms (social normsdepreciate if notaugmented periodically). Once harvesting has increased to a certainlevel, the landed farmer re-enforces social norms, thereby leading toits sharp decline as the stock of social norms increases. Note that thetime spent reinforcing norms is time lost in farming and thereforethere is an opportunity cost associated with enforcing social norms.Since we have assumed a linear effect of enforcement effort on socialnorm accumulation,we observe this kind of discontinuous enforcementpattern. When enforcement costs are non-linear, the farmer would beinvesting continuous efforts towards norm accumulation. Comparedto the base case, several scenarios lead to higher harvesting patterns.For instance, when the accumulated social norms are less effective indelivering punishment to the harvester (see scenario named ‘phi1 =0.5’, where phi1 refers to the parameter ϕ1), the harvesting pattern ishigher as well. On the contrary, when the established social norms arevery effective in punishing (see scenario named ‘phi1 = 0.9’), the har-vesting pattern is lower than the base case. There are some other sce-narios too that lead to lower harvesting than the base case. When the

0

20

40

60

80

100

120

140

160

180

200

1 3 5 7 9 11 13 15 17 19 21 23 25

Wag

es(T

hous

and

Rupe

esPe

rYea

r)

T

base case

s0=75

Fig. 7.Wages obtained based upon

effect of human capital on wages is lower (see scenario ‘chi1 = 50’,where chi1 stands for the parameter χ1), harvesting is lower. Lowerharvesting, obviously, must come through a higher social norm obtain-ed under this scenario, and we will explore the reason for this soon.Also, a lowmean rainfall of 300 mm as compared to the base case rain-fall of 400mm leads to lower harvesting pattern. Again, since we do notconsider the effect of reduced rainfall on CPR stock health, it must bethat the reduced harvesting is coming through a higher social normestablished under this scenario. A lower maximum wage potential inthe formal sector (m0 = 400) also leads to reduced harvesting througha higher social norm outcome. Finally, a lower starting level of soil qual-ity (s0= 30) as compared to the base case starting value of s0 = 40 alsoleads to higher social norms and therefore lower harvesting effort. Sce-narios that lead to a higher harvesting pattern than the base case arewhere the initial soil quality is higher (s0 = 70) and when the relation-ship governing the norm establishing effort is less effective (v = 0.25and v = 0.5 compared to the base case value of 1).

The respective social norm stock outcomes are depicted in Fig. 2. Thetimepath of social norms also follows a similar pattern as the harvestingpattern exceptwith one difference— norms are initially declining underthose scenarios whereas harvesting initially increases and vice versa.

Fig. 3 depicts the stock of CPR under the same scenarios. As is evidentfrom the graphs, all scenarios lead to an eventual long run increase inthe stock of CPR. This reaffirms the beneficial linkage effect establishedin the model which the stock of CPR has on soil quality and hence oncrop productivity. Fig. 4 depicts the time paths of soil qualities forthese scenarios. Soil quality unlike the stock of CPR declines in thelong run under all scenarios. Since we have assumed a non-linear feed-back effect that CPR stock has on soil quality, a higher initial stock of CPR(x0 = 100) has a much better long run impact on soil quality as com-pared to a lower starting level of soil quality (s0=30). Since, soil qualityoutcomes are related to CPR health which in turn is linked to harvesting

27 29 31 33 35 37 39 41 43 45 47 49 51ime

x0=50 x0=100

s0=30 low rain

human capital accumulations.

149R. Ranjan / Ecological Economics 105 (2014) 139–153

effort, the resulting outcomes seen for soil quality are merely a reflec-tion of how social norms are established under these scenarios. Whenthe acquired human capital is not effective in delivering wages in theformal sector (that is, it takes a higher human capital stock to achievethe same level of wage outcome), the farmer invests in higher socialnorm accumulating efforts instead. Note that formal sector wages pro-vide an alternate source of revenue through the education of their chil-dren, so if farmers do not see much hope from educational investment,they would try to protect their only other source of income, the agricul-tural income. This explains a higher social norm investment (and aresulting higher CPR stock as well as a relatively higher soil quality)under this scenario. When the starting level of soil quality is low at(s0 = 30), we observe a low harvesting effort through a higher socialnorm investment and a resulting higher CPR level. However, the timepath of soil quality still declines (though at a less steep rate).

Human capital outcomes are presented in Fig. 5. Two broad patternsemerge — one where human capital increases over time and the otherwhere it declines. Scenarios that lead to a decline in the human capital(implying no educational investment is undertaken) are ones wherethe maximum wages in the formal sector are lower (m0 = 400), orwhere a relatively higher level of human capital is needed to achievethe same level of wages. These scenarios could be thought of asrepresenting those farming families who are relatively disadvantagedin terms of their human capital augmenting skills or other social net-works that makes finding jobs with higher wages difficult. When suchfamilies foresee lower future wages from acquiring human capital, nat-urally, they will discount opportunities presented by human capitalaugmentation and concentrate on more traditional sources of incomesuch as through agriculture.

The time path of crop outcomes is depicted through Fig. 6. The annu-al fluctuations in output occur due to the rainfall pattern that has a base

0

20

40

60

80

100

120

140

160

180

200

1 3 5 7 9 11 13 15 17 19 21 23 25

Wag

es(T

hous

and

Rupe

esPe

rYea

r)

T

base case

chi1=45

v=.25

chi1=50, x

Fig. 8. Time paths of wages compared under a combination

case mean of 400 mm and a standard deviation of 100 mm. The highestcrop outcome is possible under a higher soil quality scenario (s0 = 75),followed by the scenario where the CPR stock is at its maximum carry-ing capacity of 100. Notice the breaks in crop outputs in certain years.This happenswhen the farmer invests all their time in social normaccu-mulation rather than agriculture. In certain scenarios they split theirtimes between farming andnormaccumulation in each year. The lowestcrop outputs aremade possible when the soil quality is very low at s0=30 and when the CPR stock is low at x0 = 50.

Figs. 7 and 8 depict the wages that materialize from human capitalaccumulations under the scenarios performed above. Note that (inFig. 7) there is one scenario (low rainfall) that leads to zero wages. Weobserved earlier that this scenario led to no human capital accumula-tion. When rainfall is low, crop income is low too, which reduces cashavailability to finance education. The fact that crop output is low alsomeans that the farmerwould need to spendmore effort enforcing socialnorms in order to avoid any further soil erosion. That is the reason wesee a very high level of social norm (as well as a low level of relativesoil erosion) under this scenario. The scenarios that lead to high wageoutcomes are where soil quality is higher to begin with (s0 = 75), andwhere starting level of forestry stock is lower (at x0= 50). The latter re-sult is surprising as one would expect low CPR stock to lead to high soilerosion and hence discourage educational effort. Soil erosion is indeedvery high under this scenario and resulting crop income one of the low-est. However, the logistic growth function assumed for the CPR dynam-ics makes the difference in this case. Note that the starting low level ofstock implies a relatively higher growth rate in forest stocks whichleads to increasing stock of CPR (see Fig. 3). Therefore, even thoughthe soil degradation is much higher, it eventually starts to slow downand the long run soil quality is not much different from most of theother scenarios. One of the lowest wages (ignoring the cases where

27 29 31 33 35 37 39 41 43 45 47 49 51ime

chi1=50

v=.5

chi1=50, s0=70

0=100

of soil and CPR stocks and human capital effectiveness.

150 R. Ranjan / Ecological Economics 105 (2014) 139–153

wages are zero) is obtainedwhen the soil quality is lowat s0=30. A lowstock of CPR only indirectly affects crop output through increasing soilerosion, however, a low level of soil quality does much more damagewhich is immediate. This explains a lower educational attainment andhence a lower long-term wages obtained under this scenario.

Fig. 8 depicts a fewmore outcomes for wages where we explore theimplications of the relative effectiveness of human capital in ensuringhigh wages in combination with soil and CPR stocks. Note that a highervalue of chi1 (chi1=50) discourages educational investment as it takestoo long to obtain a threshold level of human capital beyond whichwages rise significantly. Having a higher endowment of CPR stock (seescenario x0 = 50, chi1 = 50) does not help with ensuring higherwages, aswages still turn out to be zero in the long term. However, hav-ing a higher endowment of soil quality leads to higher wages (eventhough they are the lowest in the category of cases where wages arepositive in the long term). This once again emphasizes the relative im-portance of soil quality as compared to CPR stock in determiningfarmers' long-term livelihood outcomes.

We next explore the implications of climate change risk in themodel. Assume that the hazard rate λ tð Þ of the climate event is 0.1.Given this rate, the probability that such a climate event would occurbefore 15 years would be 75% and the probability of the same happen-ing before the next 8 years would be 50%. Calibrating the post-climatechange value function comprising more than two state variables be-comes challenging. Hence, we simplify a little by making assumptionsof different types of risk that the farmer could face and then calibratethe value functions separately under these assumptions.

The calibrated value functions are derived under various assump-tions. In the first case when the carrying capacity of the CPR in the

0

10

20

30

40

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19 21 23 25

CPR

Stoc

k (T

hous

and

Tonn

es)

T

base case

risk case_rain_mean=300mm

risk case_x0=40

Fig. 9. Stocks of CPR generated unde

post-climate change scenario is assumed to be reduced to 75, thepost-climate change value function is given as:

Vpost x tð Þ; E tð Þð Þ ¼ 75:98þ 0:2999 � x tð Þ þ 4:24 � E tð Þ−0:001548

� x tð Þ2−0:006918 � E tð Þ � x tð Þ−0:1974 � E tð Þ2: ð37Þ

Under this scenario, it is assumed that there is an exogenous risk ofclimate change leading to a sudden reduction in the CPR carrying capac-ity, followingwhich the farmer faces the challenge of re-establishing so-cial norms as the accumulated norms are assumed lost in the suddenshock generated by the temporary loss of livelihoods for the landlesscategory. In the post-shock event the landed farmer re-optimizes overtheir labor, education and norm accumulation decisions. The post-event value function is calibrated over starting values of human capitaland the stock of CPR that the farmer has at the time the event material-izes. We ignore the stock of financial wealth in the post-value calibra-tion as wealth was found to have no effect in the pre-shock outcomes.The value function is calibrated by repeatedly solving for the obtainedutility outcomes for various possible combinations of CPR stock andhuman capital stock that the farmer may have remaining at the timethe climate event arrives. A polynomial function of degree two is usedto fit a curve around the obtained outcomes (using the cftool option inMATLAB).

In the next simulation, it is assumed that the climate change relatedshock pertains to a sudden reduction inmean rainfall to 300mm(whilethe carrying capacity of the CPR remains unaffected). When the mean

27 29 31 33 35 37 39 41 43 45 47 49 51ime

risk case_k=75

risk case_p=40

r climate change risk scenarios.

0

1

2

3

4

5

6

7

8

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53

Soci

alN

orm

Time

base case low rain

risk case_k=75 risk case_rain_mean=300

risk case_p=40 risk case_x0=40

no risk case_x0=40

Fig. 10. Social norm outcomes under climate change risk.

151R. Ranjan / Ecological Economics 105 (2014) 139–153

rainfall is reduced to 300mm, the new post-climate change value func-tion is calibrated as:

Vpost x tð Þ; E tð Þð Þ ¼ 80:72� 0:01033 � x tð Þ þ 4:997 � E tð Þ þ 0:0006844� x tð Þ2−0:001757 � E tð Þ � x tð Þ−0:3123 � E tð Þ2: ð38Þ

Wealso, try a positive risk scenario, where the farmer expects the ar-rival of an eventwhichwould double the crop price in the future.Whenthere is a chance that future crop prices will double, the new post-climate change value function is given as:

Vpost x tð Þ; E tð Þð Þ ¼ 94:31þ 0:02684 � x tð Þ þ 1:903 � E tð Þ þ 0:0007215

� x tð Þ2−0:0008314 � E tð Þ � x tð Þ−0:02302 � E tð Þ2:

When future climate change leads to a reduction in stock of CPR to40, the post-event value function is calibrated as a function of stock ofsocial norms and human capital. Note that under this scenario we as-sume that the social norms are not lost upon arrival of a climate changerelated shock in the future which leads to a loss of CPR stock (instead ofits carrying capacity as assumed earlier). The new post-climate changevalue function is calibrated as:

Vpost n tð Þ; E tð Þð Þ ¼ 83:76þ 0:7982 � n tð Þ þ 4:118 � E tð Þ−0:03878

� n tð Þ2−0:05003 � E tð Þ � n tð Þ−0:2271 � E tð Þ2: ð39Þ

Finally, when climate change leads to a CPR stock reduction to 60,the post-climate change value function is calibrated as:

Vpost n tð Þ; E tð Þð Þ ¼ 84:9þ 0:9846 � N tð Þ þ 4:124 � E tð Þ−0:05737

� N tð Þ2−0:07589 � E tð Þ � N tð Þ−0:2225 � E tð Þ2: ð40Þ

The resulting outcomes under risk are presented in Figs. 9 through11. In Fig. 9, a risk of future reduction in carrying capacity to 75 leadsto lower outcomes for the CPR stock over time. Similarly, when therisk involves a reduced mean rainfall of 300 mm, a lower CPR stock ismaintained. A doubling of crop price in the future also does not encour-age higher CPR stock. A lower CPR stock occurs due to lower investmentin social norms (see Fig. 10). Since, the assumption under all theseabove scenarios involves a loss in accumulated norms with the arrivalof a climate change related event, farmers do not invest in socialnorms as much as they would under the absence of risk. As Fig. 11 de-picts, a higher agricultural price of 40 rupees per kilo leads to higherhuman capital as compared to the base case in the absence of anyrisks. However, when the possibility of prices doubling in the future isincluded as a risk, human capital investment declines.

6. Conclusion

Common pool resources have been widely studied with respect totheir sustainability aspects as well as the factors that lead to their desta-bilization or extinction. Climate change related events such as repeateddroughts or frequent flooding can add to the challenges of managingCPRs as they could abruptly reduce their carrying capacity or their

-0.4

0.1

0.6

1.1

1.6

2.1

2.6

3.1

3.6

4.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73

Hum

anCa

pita

l

Time

base case risk case_p=40 p=40_no risk

Fig. 11. Stocks of human capital compared for climate change risk scenarios.

152 R. Ranjan / Ecological Economics 105 (2014) 139–153

stocks or both. Additionally, such changes could impact on the produc-tivity and livelihoods of communities directly or indirectly dependentupon CPR. Climate change also directly stresses and challenges tradi-tional forms of obtaining livelihoods in rural areas by adversely affectingagricultural productivity through causing repeated droughts. This forceslarge scale migration and occupational changes in rural communities.When faced with such challenging events, how should natural re-sources be managed and maintained so as to assist with short-term oc-cupational adjustments while maintaining long-term livelihoodresilience? This is the question we took up in this paper.

Several interesting insights emerge from the theoretical model andthe ensuing numerical example. First, when environmental degradationcaused by CPR depletion affects crop productivity, optimal strategy re-quires that social norms be maintained high enough to discourageoverharvesting of resources. However, when farmers cannot effectivelyenforce social norms, a reduced CPR stock results in lower crop incomesand hence welfare. Low rainfall discourages human capital investmentas there is not enough cash available to pay for education. Whereas, alow level of CPR stock in some cases may not be detrimental tohuman capital accumulation. For farmers, who are less advantaged interms of converting their human capital into tangible wages, it doesmake a difference whether they own a higher endowment of CPRstock or are having a higher soil quality. For such category of farmers,a higher endowment of CPR stock may not lead to high wages whereasa better soil quality can still ensure a livelihood transition.

The presence of a risk of future loss to the CPR carrying capacity or itsstock leads to lower enforcement of social norms thereby affecting cropincome and human capital outcomes. Generally, it is found that a risk ofreduced rainfall or a risk of reduced carrying capacity is detrimental tohuman capital outcomes and leads to lower welfare for the farminghousehold.

Wemade a number of simplifying assumptionswhile deriving theseresults. In reality, common pool resources in different regions vary sig-nificantly in the challenges and management regimes that they face.The ability of one group to enforce and maintain norms could be se-verely diminished due to a number of factors including migration(in both landed and landless communities), outside interventions,high cost of enforcement or situations where CPR depletion hasalready led to significant soil deterioration. When faced with lowproductivity in agriculture, farmers may be able to adapt to a certainextent by altering crop mixes and supplementing their incomesthrough seasonal migration. Yet, the potential of climate changerelated events to exacerbate CPR management challenges shouldnot be taken lightly and further research would be needed to ensureadvanced preparedness.

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