The runoff from agricultural fertilizers contains compounds that
damage local watersheds. Suppose the private marginal costs of
production and the demand (marginal benefit) in the market for
fertilizer are as follows:

MC_P = 20 + 0.5Q
MB = 50 − 0.25Q

The social marginal cost of production is:

MC_S = 30 + 0.75Q

a. What level of output will be produced in a competitive free market?

b. What is the allocatively efficient level of output?

c. What is the marginal external cost at the competitive freemarket equilibrium?

d. What is the marginal external cost at the allocatively efficient level of output?

e. What level of emissions tax ($ per unit produced) would lead to the allocatively efficient level of output?