Suppose that the marginal benefit associated with corn production is MB = 2.5. T

Question

Suppose that the marginal benefit associated with corn production is MB = 2.5. The marginal private cost of production is MPC = 2 + 0.1Q, where Q measures bushels of corn produced in thousands. The marginal damages caused by pollution in corn production are given by MD = 0.05Q.

a. Compute the privately optimal output and the socially optimal output.

b. Compute new solutions for an increase in MB to MB = 3. Explain what has happened and why.

c. Demonstrate the effects of an increase in MD to MD = 0.075 compared to the solutions in part a.

Explanation / Answer

nswer:

a. Privately optimal output rate is found by setting the private marginal benefit equal to

the private marginal cost: 2.5 = 2.0 + 0.1Q. Solving for Q we obtain Q=5. The

socially optimal output rate is found by setting the private marginal benefit equal to

the marginal social cost: 2.5 = 2.0 + 0.1Q +0.05Q. Solving for Q provides Q=3.33.

b. When the marginal benefit rises to MB

=3, the private solution changes to Q=10 and

the social solution changes to 6.67. Since the marginal benefit has risen, larger

outputs can be justified (recall that both

marginal private cost and marginal social

cost are rising with output).

c. A larger marginal damage reduces the socia

lly optimal solution in part (a) to Q=2.86.

The privately optimal solution is unaffected, of course, because it does not take

marginal damages into account.

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