8.2 A competitive fertilizer market has many small firms. The inverse demand function for fertilizer is p = 40 - 2Q, where Q is a ton of fertilizer and p is the price per ton of fertilizer. The market supply curve—the sum of the private marginal cost curves of all the firms—is MCp = Q + 4. The fertilizer industry is a major source of water pollution and the marginal external damage, MCx, caused by the industry to the communities near the fertilizer firms is $6 per ton of fertilizer produced.

a. Create a spreadsheet with column headings for output Q, price p, private marginal cost MCp, marginal cost of pollution MCx, and social marginal cost MCs = MCp + MCx. Fill in the spreadsheet for Q = 1, 2, 3, p 20.

b. Determine the equilibrium output and price in the competitive fertilizer market if firms do not have to pay for the pollution they create.

c. Determine the socially optimal amount of fertilizer.

d. What per unit tax can the government impose to generate the socially optimal amount of output?