Consider the case of a corn producer. This producer is a monopolist in the corn market. Since corn production uses significant amounts of fertilizers, it negatively affects the environment. Recall that, when a firm is a monopolist, it reduces its production so that it can increase price; although it sells fewer units, the higher price more than makes up for the reduced volume. Consumers lose, and total welfare is reduced, due to the higher price and lower quantity. A pollution externality, in contrast, implies excess production above the socially optimal quantity.
a. Draw a supply-demand figure for a firm with the demand curve Q = 10-P, and marginal cost curve MC = 2 (based on total costs C = 2 x Q). If this were not a monopoly, what would be the equilibrium price and quantity? Calculate the firm’s total revenue and producer surplus. Also calculate consumer surplus. Recall that the formula for net social benefits is consumer surplus plus producer surplus minus damages. Calculate that value.
b. Suppose that, instead, the firm decided to act like a monopolist and restrict output. It produces 4 units and charges $6 for each unit. Calculate the producer surplus, consumer surplus and net social benefits. Are net benefits higher or lower? Is the firm better or worse off?
c. Now let’s consider the scenario where production has some related damages in the form of pollution. Suppose the firm produces marginal damages of $4/unit. For both (a) and (b), recalculate net benefits to account for the social damages.
d. Find the new efficient equilibrium, now that social marginal costs are $6/unit (MCpriv +MCex. Calculate the producer surplus, consumer surplus, damages, and net social benefits.
e. If forced to pay social marginal costs, a monopolist will produce 2 units and charge $8 for each unit. Calculate the producer surplus, consumer surplus, damages, and net social benefits.
f. Compare the results for (c), (d), and (e). Rank them from the highest net benefits to the lowest.
g. A regulator who can break up monopolies is examining this situation. Compare net benefits for the monopolist who pollutes [the recalculation for the monopolist in Part (c)] with the competitive firm that pollutes [the recalculation for the competitive firm in Part (c)]. Will the regulator improve net benefits by breaking up the monopoly?
h. Now assuming monopoly production, compare net benefits for the monopolist who pollutes [the recalculation for the monopolist in (c)] with net benefits for the monopolist who pays the full costs of pollution in (e). Will a regulator increase net benefits by taxing pollution?
i. Does fixing a market failure always improve welfare, compared to not fixing it?