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?