Textbook Problem

Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its new DVD:

Demand: P = 1,000 - 10Q

Total Revenue: TR =1,000Q - 10Q²

Marginal Revenue: MR = 1,000 - 20Q

Marginal Cost: MC = 100 + 10Q,

where Q indicates the number of copies sold and P is the price in Ectenian dollars.

a. Find the price and quantity that maximize the company’s profit.

b. Find the price and quantity that would maximize social welfare.

c. Calculate the deadweight loss from monopoly.

d. Suppose, in addition to the costs above, the director of the film has to be paid. The company is considering four options:

i. a flat fee of 2,000 Ectenian dollars.

ii. 50 percent of the profits.

iii. 150 Ectenian dollars per unit sold.

iv. 50 percent of the revenue.

For each option, calculate the profit-maximizing price and quantity. Which, if any, of these compensation schemes would alter the deadweight loss from monopoly? Explain.