Based on market research, a film production company obtains the following information about

the demand and production costs of its new DVD:

Price = 1000 - 10Q

Total Revenue =1000Q - 10Q2

Marginal Revenue = 1000 - 20Q

Marginal Cost = 100 + 10Q

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

(a) Find the price and quantity that maximizes 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 2000 cents

ii. 50 percent of the profits

iii. 150 cents 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 a monopoly? Explain.