The Economics of Climate Change C 175 Learning Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 39 The Economics of Climate Change C 175 Learning In the following We continue with risk We work with a risk neutral agent U M M Justification Still complicated enough Shows that value from anticipated learning even if no risk aversion Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 40 The Economics of Climate Change C 175 Learning An important characteristic of uncertainty is that it generally resolves over time We learn Two ways y to incorporate p that we learn 1 2 Naive way we do not anticipate that we learn we only consider that we learn after new information arrives Sophisticated way we anticipate i i that h we will ill learn l we already incorporate in today s plans that we will learn in future How does such an anticipation change today today ss decisions Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 41 The Economics of Climate Change C 175 1 Learning and Option Value Given is following project Invest USD I 60 now and in the following period receive either USD R 100 with p R 100 5 or R 50 with p R 50 5 Return R is random variable We discount future period with factor D 1 Find expected return of project project E I D R 60 0 5 D 100 50 75 D 60 Say discount factor D 9 D 9 8 8 then E I D R I D R 7 5 7 5 project has positive expected payoff So should we invest Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 42 The Economics of Climate Change C 175 1 Learning and Option Value Assume we can only do project once E g install a particular new abatement technology in a power plant not sure how much it abates how much we gain in carbon credits Idea What iff uncertainty y resolves at beginning g g off next p period E g we know how well abatement technology works by watching neighbor plant trying the technology We W wait i till ill next period i d and d only l iinvest if R 100 R That can be even better Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 43 The Economics of Climate Change C 175 1 Learning and Option Value Uncertainty resolves at beginning of next period We wait till next period and only invest if R 100 In the next period we then expect the return E I D R 5 I D 100 5 0 5 60 100 D 30 50 D 5 60 D From our present perspective next period payoffs have to be discounted Thus us eexpected pec ed net e p present ese va value ue of investing ves g in seco second d pe period od iff R 100 00 iss E D I D2 R 30 50 D D Note that I became random variable as well Random variable R changed pays 100 only in case we invest Say D 9 then E D I D2 R 13 5 Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 44 The Economics of Climate Change C 175 1 Learning and Option Value Thus we either have expected return by investing immediately E I D R 75 D 60 and with D 9 a return of 7 5 Or we have expected return by waiting until uncertainty resolves and only investing if high payoff 3 5 D D E D I D2 R 30 50 and with D 9 a return of 13 5 Thus if we can only invest once do not invest in present period despite expected return positive invest i iin second d period i d if and d only l if return is i high hi h Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 45 The Economics of Climate Change C 175 1 Learning and Option Value The different in value between executing project immediately E I D R 75 D 60 And the value from waiting until uncertainty resolves E D I D2 R 30 50 D D is called an option value OV note not the same as what Kolstad calls option value Here OV 30 50 D D 75 D 60 60 105D 50D2 and with D 9 we find OV 13 5 7 5 6 OV is i the h value l off having h i the h option i to wait i ffor uncertainty i to resolve l Remark More precisely it should therefore be defined as OV Max 0 OV the option to invest is only exercised if OV is positive Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 46 The Economics of Climate Change C 175 2 Learning and Optimal Mitigation Level Preparation Superstylized Climate Change Impact Model static warm up GHG emissions x Money measured benefits from emissions cheaper production saved abatement costs x2 x 2 Money M measured d damage d f from GHG emissions i i x2 Damage parameter is uncertain a random variable Interested in finding optimal emissions x Assume risk neutrality U M M RRA See problem 3 2 x2 max x x 2 x 2 where E is expectation with respect to the random variable Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 47 The Economics of Climate Change C 175 2 Learning and Optimal Mitigation Level To proceed need assumption with respect to values and likelihood of Assume is either o or 1 with equal q p probabilityy p 0 5 and p 1 5 Then x2 max x x 2 x 2 x2 x2 2 max 5 x 5 x x x 2 2 x2 x2 max x x 2 2 1 x 2 Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 48 The Economics of Climate Change C 175 2 Learning and Optimal Mitigation Level Note that we neglected g the underlying y g wealth M M does not matter under risk neutrality for deciding on x That is because x2 max M x x 2 x 2 x2 M max x x 2 x 2 So that M does not matter for the maximization drops out in first order condition for maximum Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 49 The Economics of Climate Change C 175 Variation Homework Keep other assumptions but now assume p p 0 1 and 3 p 5 2 3 Solve x2 max x x 2 x 2 and find whether the optimal GHG emission x is smaller or larger than before Spring 09 UC Berkeley Traeger 5 Risk and Uncertainty 50 The Economics of Climate Change C 175 2 Learning and Optimal Mitigation Level Dynamic Model Model dynamic Assume two periods no discounting 2 x in each period benefits xi i 2 where i 1 2 damage only in second period damage depends on aggregate emissions in both periods stock x1 x2 2 In period 1 is unknown and p 0 5 and p 1 5 Distinguish g two settings g 1 Also in period 2 is unknown no …