Calculate the consumer surplus-producer surplus

Question

Assignment:

The process of tanning leather creates toxic byproducts that pollute the local water supply. Suppose that a city's tanneries (Le., producers) compete in a perfectly competitive market, facing demand given by p(Q) = 60 - 1/2Q and a constant (private) marginal cost of 10. Leather production imposes external costs equal to EC(Q) = 1Q2.

a. Draw a clearly labeled graph representing this market. Include:

• The private marginal benefit curve (i.e., the demand curve)

• The private marginal cost curve (i.e., the supply curve)

• The external marginal cost curve

• The social marginal cost curve

Include axis labels for all points where these curves intersect each other or the axes.

b. On your graph from part a, mark the competitive quantity (Q_c) and price (p_c). Shade in the deadweight loss and compute its area. Then calculate the consumer surplus, producer surplus, external cost, and (finally) total surplus.

c. Find the socially optimal quantity (Q_s.). What is the private marginal cost at Q_s? What is the external marginal cost at Q_s? What is the social marginal cost at Q_s?

d. Suppose that the city imposes a corrective tax t on the tanneries for each unit of output they produce. Find the value t*. that results in the socially optimal amount Q_s. being produced. Compute consumer surplus, producer surplus, tax revenue, and external cost under this tax. How does the total surplus compare with the total surplus in part b?