18.9 Suppose the government wished to combat the undesirable allocational effects of a monopoly through the use of a subsidy.

a. Why would a lump-sum subsidy not achieve the government’s goal?

b. Use a graphical proof to show how a per-unit-of-output subsidy might achieve the government’s goal.

c. Suppose the government wishes its subsidy to maximize the difference between the total value of the good to consumers and the good’s total cost. Show that to achieve this goal it should set

, where t is the per-unit subsidy and P is the competitive price. Explain your result intuitively.