1: Pigouvian tax and uncertain damages Suppose marginal savings from pollution emissions e are known, MS(e) = 36 9e. However, marginal damages are uncertain: MDH(e) = 16e with probability 0.3 MDL(e) = 6e with probability 0.7 1. What is the expected marginal damage function? Draw a diagram showing this function, along with MDH(e) and MDL(e). Include the marginal savings function. 2. What is the optimal Pigouvian tax rate, in expectation? Show it on your diagram. 3. If the tax rate you calculated in part 2 is imposed, what is the expected DWL? Question 2: Tradeable emissions permits Assume an economy of two firms. The two firms pollute. Firm one has a marginal savings function of MS1(e1) = 5 1 2 e1 where e1 is the quantity of emissions from the firm. Firm two has a marginal savings function of MS2(e2) = 11e2. The aggregate marginal damage to all consumers is MD(E) = 1 3E, where E the total amount of emissions (E = e1 + e2). Note the similarity between this question and Q4 in Tutorial 4. 1. Suppose the government imposes an emissions quota. The quota is at a level such that each firm must reduce pollution to e1 = e2 = 7.5. Is this a least-cost way of achieving the pollution reductions? 2. Say the government allows the quotas to become tradeable permits. Each firm is issued with 7.5 permits. Draw a diagram showing the trade between firms, and shade the cost savings from allowing this trade. 3. Calculate the trade in permits that you expect. What would be the competitive price of the tradable permits? Hint: you will need to use the fact that 15 = e1 + e2