The following figure shows the demand (D), marginal revenue (MR), and marginal cost (MC) curves for a monopolist.

-Refer to the figure above.The monopolist is forced to charge the competitive price,but the government agreed to compensate the monopolist for its loss in producer surplus,in comparison to the profit-maximizing outcome.What is the amount of compensation per unit of output traded?

Question

The following figure shows the demand (D), marginal revenue (MR), and marginal cost (MC) curves for a monopolist.
 
-Refer to the figure above.The monopolist is forced to charge the competitive price,but the government agreed to compensate the monopolist for its loss in producer surplus,in comparison to the profit-maximizing outcome.What is the amount of compensation per unit of output traded?

Quizplus · Accepted Answer

When the monopolist is forced to charge the competitive price, its profit-maximizing output will be where MR = MC, which is Q₁. At this output level, the monopolist would have produced Q₃-Q₁ less than the profit-maximizing level, resulting in a loss of (Q₃-Q₁) x (P₃-P₁) in producer surplus. The compensation per unit of output traded would be the amount of this loss divided by the total output Q₃:
[(P₁-P₃) x Q₁ - ((P₁-P₄) x (Q₃-Q₁)/2)]/Q₃
Simplifying this expression, we get:
[(P₁-P₃) x Q₁ - (P₁-P₄) x (Q₃-Q₁)/2]/2
which is option B.

The Following Figure Shows the Demand (D), Marginal Revenue (MR)