Willingness to Pay for a Risk Reduction

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1 The Economics of Climate Change C 75 Willingness to Pay for a Risk Reuction Sring 0 C Berkeley Traeger 5 Risk an ncertainty

2 The Economics of Climate Change C 75 Back to Risk We will mostly treat the category of risk/likelihoo/robabilities: Easiest to cature mathematically Sufficiently rofoun to erive interesting insights Sring 0 C Berkeley Traeger 5 Risk an ncertainty 5

Easiest to cature mathematically Sufficiently rofoun to erive

3 The Economics of Climate Change C 75 Willingness to Pay for a Risk Reuction oel: Two ossible outcomes Probability of amage e.g. Great Barrier reef ea by 050 ==5 with robability =Pr=5=.5 =0 with robability =Pr=0=.5 is ranom variable an is magnitue of ossible amage in $ Baseline consumtion = Sring 0 C Berkeley Traeger 5 Risk an ncertainty 6

e.g. Great Barrier reef ea by 050 ==5 with robability =Pr=5=.

4 The Economics of Climate Change C 75 Willingness to Pay for a Risk Reuction oel: Two ossible outcomes Probability of amage e.g. Great Barrier reef ea by 050 ==5 with robability =Pr=5=.5 =0 with robability =Pr=0=.5 is ranom variable an is magnitue of ossible amage in $ Baseline consumtion = Execte utility of lottery Examle of Risk neutrality where =: 3 Sring 0 C Berkeley Traeger 5 Risk an ncertainty 7

5 Willingness to Pay for a Risk Reuction The Economics of Climate Change C 75 tility of lottery SALL Change in risk: > *=+Δ SALL Change in risk: > =+Δ ] [ ] [ * * * ] [ ] [ So the change Δ causes a welfare change: * * Sring 0 C Berkeley Traeger 5 Risk an ncertainty 8

Change in risk: > =+Δ ] [ ] [ * * * ] [ ] [ So the change Δ causes

6 Willingness to Pay for a Risk Reuction The Economics of Climate Change C 75 tility of lottery Similarly : Similarly : SALL Change in baseline consumtion/money: >*=+ Δ * * * ' With ste intuition: small amount of consumtion change Δ times execte marginal utility erive from Δ So the change Δ causes a welfare change: ' * Sring 0 C Berkeley Traeger 5 Risk an ncertainty

With ste intuition: small amount of consumtion change Δ times execte marginal utility erive

7 The Economics of Climate Change C 75 Willingness to Pay for a Risk Reuction Question: How much Δ willing to sen at most to reuce risk by Δ? Answer: Welfare change cause by Δ together with welfare change cause by Δ shoul leave agent inifferent to no change Hence: From which follows: 0 ' ' Sring 0 C Berkeley Traeger 5 Risk an ncertainty 30

Answer: Welfare change cause by Δ together with welfare change cause by Δ shoul

8 The Economics of Climate Change C 75 Willingness to Pay for a Risk Reuction ' Interretation: The willingness to ay for a risk reuction Increases in the utility loss cause by the amage ecreases in the execte value of money which agent has to give u Sring 0 C Berkeley Traeger 5 Risk an ncertainty 3

Increases in the utility loss cause by the amage ecreases in the execte

9 Willingness to Pay for a Risk Reuction: Examle The Economics of Climate Change C 75 ' Risk neutral agent =: 5 Sring 0 C Berkeley Traeger 5 Risk an ncertainty 3

10 Willingness to Pay for a Risk Reuction: Examle The Economics of Climate Change C 75 ' Risk neutral agent =: 5 Risk averse agent = : Sring 0 C Berkeley Traeger 5 Risk an ncertainty 33

neutral agent =: 5 Risk averse agent = : 5 5 3

11 Willingness to Pay for a Risk Reuction: Homework The Economics of Climate Change C 75 ' Assume =Pr=5=. Risk neutral agent =: Risk averse agent = : Sring 0 C Berkeley Traeger 5 Risk an ncertainty 3

12 Willingness to Pay for a Risk Reuction: Homework The Economics of Climate Change C 75 ' Assume =Pr=5=. Risk neutral agent =: 5 Risk averse agent = : Sring 0 C Berkeley Traeger 5 Risk an ncertainty

Risk neutral agent =: 5 Risk averse agent = : 0 5.

13 The Economics of Climate Change C 75 Intuition Risk Neutral vs. Risk Averse ' Without loss of generality: if you woner why that is without loss > office hour Assume that an coincie for risk averse an risk neutral agent Then enominator ecies: Risk neutral agent has same marginal utility at an Sring 0 C Berkeley Traeger 5 Risk an ncertainty 36

office hour Assume that an coincie for risk averse an risk neutral agent Then

14 The Economics of Climate Change C 75 Intuition Risk Neutral vs. Risk Averse ' Without loss of generality: if you woner why that is without loss > office hour Assume that an coincie for risk averse an risk neutral agent Then enominator ecies: Risk neutral agent has same marginal utility at an Risk averse agent has Higher marginal utility at than risk neutral agent Lower marginal utility at than risk neutral agent > > ore weight on high outcome ecreases execte marginal utility that risk averse agent erives from the ollar he has to give u to reuce > ore weight on low outcome increases execte marginal utility that t risk ik averse agent erives from the ollar he has to give u to reuce Sring 0 C Berkeley Traeger 5 Risk an ncertainty 37

neutral agent has same marginal utility at an Risk averse agent has Higher marginal utility at than risk neutral agent Lower marginal utility at than risk neutral agent > > ore weight

15 The Economics of Climate Change C 75 Intuition Risk Neutral vs. Risk Averse Risk averse ecision maker relative to risk neutral ecision maker: In the ba state the risk averse ecision maker is hurt relatively more by the money he gives u for the risk reuction which makes him even worse off than in the former ba state In the goo state the risk averse ecision maker is hurt relatively less by the money he gives u for the risk reuction concave utility > refers less in goo state in orer to avoi ba state It eens on robability weight of goo vs. ba state magnitue of marginal utility ifference in goo vs. ba state with resect to risk neutral agent whether risk averse agent is willing to ay more or less for risk reuction Sring 0 C Berkeley Traeger 5 Risk an ncertainty 38

reuction which makes him even worse off than in the former ba state In the goo state the risk averse ecision maker is hurt relatively less by the money he gives u for the risk reuction

Chapter 4: Elasticity

Chapter 4: Elasticity Chapter : Elasticity Elasticity of eman: It measures the responsiveness of quantity emane (or eman) with respect to changes in its own price (or income or the price of some other commoity). Why is Elasticity