Problem 8. (Misrepresented MACs and inefficiency.) The government wishes to set a carbon tax. The marginal damage of emissions is MD=5*e. The true total abatement cost function of firms is AC(a)=2*a^2 , and the initial, unabated level of emissions is =30. However, the firms understate their true total cost of abatement, and tell the government that their total abatement function is AC(a)=a^2 .

A. Derive the true MAC.

B. Derive the MAC that the firms report to the government.

C. Draw true and reported MACs, and MD in a graph where the x-axis is emissions and the y-axis is $.

D. Find the true socially optimum level of emissions.

E. Find the Pigouvian tax that the government would impose if it knew the true MAC.

F. But the government uses the reported (not the true) MAC to compute the carbon tax. What is the level of the carbon tax set by the government?

G. What is the level of the emissions at the level of the carbon tax in question E.?

H. Compute the loss experienced by the general public when the government uses the reported MAC to set the tax.

Emphasis on questions E-H. Please and Thank You!