Question

2. Market Based Methods And Uncertainty (15 points) Suppose vou had the following polluting industrv with marginal cost of reduction and marginal damages given by MCR= 24-E MD-3E Where E is the amount of emissions a) What is the optimal amount of pollution? What is the optimal pollution tax? How many permits would you issue in a cap-and-trade system b) Now suppose you were mistaken and thought that the marginal cost of reduction was more expensive than it actually is. Suppose you falsely believed that the marginal cost of reduction was MCR-28-E What would you think the optimal tax would be? What would you think the optimal number of permits would be? c) If you were uncertain about what the true MCR was which policy would cause less deadweight loss, taxes or cap-and-trade? (Note: you should not have to do any math to solve this problem d) What would be the quantity of pollution if you set a tax assuming the MCR in b, but the actual MCR is the equation in part a. What is the deadweight loss? e) What would be the quantity of pollution if you set a cap assuming the MCR in b, but the actual MCR is the equation in part a. What is the deadweight loss?

Answer 1

A) at eqm, MCR = MD

24-E = 3E

24 = 4E

E* = 6.

so optimal amount of pollution = 6,

Optimal pollution tax = MD at eqm = 6*3 = 18

permits issued = 6

B) new MCR = 28- E

Now at eqm , MCR = MD

28-E = 3E

E* = 7

New optimal tax = 3*7 = 21

new permits = 7

C) taxes always cause deadweight loss, as these are distortionary, so always prefer cap & trade policy .

D) tax set ( according to b) = 21

(While actual tax should have been = 18)

So now MCR curve shifts inwards, so new MCR`= 24-E-21

MCR` = 3-E

so now quantity of pollution = 3,

( Where MCR` = 0)

So deadweight loss: .5*(18-9)*(6-3) = 13.5

E) cap set According to b) = 7

While actual cap should have been = 6

So Quantity of pollution= 7

Deadweight loss = .5*(7-6)*(21-18) = 3/2 = 1.5