1Addendum to Lecture 14Kyoto Climate ChangeThe United States needs to reduce CO2 emissionsPADQQQ0_D = demand for CO2Q0= initial levelQt= target levelQQ01-=reduction requiredThe area AQ Q0= social cost of CO2 reduction.Mechanisms to reduce cost:1. Purchase CO2 permits from other countries (Russia), price V.2. Provide carbon reduction in less-developed countries through the clean developedmechanisms (CDMs),2MCD = marginal cost of CO2 provision of CDM.Using the target levels as benchmarks, let ƒQ denote consumption of CO2 beyond Q.ƒƒDQ= demand forAQVOQ~~120 _~D~QQQMCDMC Q DMDA()= marginal cost of quantities available through C.Equilibrium results:ƒQ CDM1= amount obtained throughƒƒQQ CO t21-=amount purchasedon marke2√QQ2= extra emissions available beyond.3Soil carbon sequestration can be added to the analysis. LetMC QSƒ() = marginal cost of sequestrationandMC QDƒ() = marginal cost of CDM.We can combine the two to form MCTby horizontal addition. The result isQVOQ~~120 D~Q~~3MCDMCSMCTQQƒƒƒƒƒƒ.Q CDMQQQQ COQCO Q12132 232=-=-==quantity provided byquantity provided by sequestrationquantity provided by buying permitsextra beyondThe Unstable Nature of Soil CarbonAfter many years of traditional tillage, an acre of land has exhausted much of itscarbon context and can absorb up to (approximately) S tons of carbon.4Let St be the amount of carbon sequestered in time t, S00=. The amount ofcarbon sequestered in year t is XSStt=-()a.Assume S ==71anda..At year 1, if no tillage is used,X17= . tons.Let DY be loss of yield because of low tillage, P be price of output, and V beprice of carbon. A farmer will apply no tillage ifaVS S PYt-()->gain from carbonloss of revenueD 0.(The model is more complex. Low tillage builds soil and increases yield in the long run,but we shall simplify.)The attractiveness of sequestration declines over time. However, if a farmerswitches to traditional tillage, bof is releasedSt. If farmers are paid V dollars only forbuildup of carbon, a farmer will use no tillage as long asaVS S PYt-()>D.There is a critical carbon level in the soil SSPYVC=-Da, and a farmer will adopt notillage if SStC<.To maintain carbon in the ground once it is introduced, we need to institute apenalty on tillage activities that will release carbon. Thus, the farmer receives V forsequestered carbon and pays a certain price for released carbon. If the price of thereleased carbon is also V, a myopic farmer (or a renter) will continue to adopt low tillagewhen5abVS S VS PYtt-()+>gain from sequestrationpenalty for emissionloss of profitdue to salesD.This formula suggests that when a farmer gains and loses based on the emissionor sequestration of carbon, the range of adoption increases to include individuals withhigh carbon storage. The formula suggests that whenSPY VSVt>--()Daba,the farmer will adopt low tillage.If PYDis very small, the denominator is negative, and the farmer will alwaysadopt. Higher carbon pay and lower output price will enhance
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