Problem 1. The government is hoping to reduce the amount of pollution in the Chesapeake Bay and determines that two firms are responsible for this pollution. For firm 1 the costs of pollution reduction are equal to 2X1 whereas for firm 2 they are constant and equal to 80.
a) Graph the industry-level marginal cost curve.
b) Which firm is reducing pollution in each range of pollution reduction x=x1+x2?
c) Suppose that the benefits of pollution reduction are equal to 180-x (with x=x1+x2). Solve for the socially efficient outcome.
d) Compare the total costs and benefits of achieving this outcome.
Problem 2. Assume that there are two firms in a local area that emit nitrous oxide into the atmosphere. Given their current level of activity, each firm could reduce its pollution though at some cost. The costs to firms A and B of reducing pollution are 40+4xA and 60+2xB, respectively, with the total amount of pollution reduction equal to xA+xB.
a) Graph the identity-level marginal cost curve assuming that each unit of pollution reduction is performed by the firm with the lowest cost.. Be sure to specify which firms are reducing pollution in each range of x.
b) Now suppose that the government releases a report showing that the marginal benefit of pollution reduction is equal to 100-x. Solve for the socially efficient value of x.
c) By how much does each firm reduce its level of pollution in this case?
d) How do the benefits of this pollution reduction compare with the costs?
e) Repeat parts b, c, and d assuming that the total amount of pollution reduction is the same. But in this case assume that each firm performs an equal amount of pollution reduction.