1. Monopoly
Suppose that the (inverse) market demand curve for a new drug, Adipose-Off, designed to painlessly reduce body fat, is represented by the equation P=100-2Q, where P is the price in dollars per dose and Q is the annual output. (The marginal revenue curve is thus given by the equation MR=100-4Q.) Suppose also that there is a single supplier of the drug who faces a marginal cost, as well as average cost, of producing the drug, equal to a constant $20 per dose.
(1) What are the monopolist's profit-maximizing output and price?
(2) What is the resulting deadweight loss relative to the competitive outcome? Give quantitative answers, please.
(3) Suppose that the government levies an excise tax of $5 per dose on the monopolist.
(a) What would happen to the monopolist's profit-maximizing output and price? Calculate the new output and price, please.
(b) What would happen to consumer and producer surplus? Calculate the changes, please.
(c) How much money would the government collect due to the tax (that is tax revenue)?
(4) Calculate the Lerner Index for the monopoly described in question (1) above (before tax).
2. Make profit or not?
The City of Berkeley is currently considering alternative ways of providing cable service to its citizens. Based on an econometric analysis of several recently awarded cable franchises in other cities, economists have determined that the total cost, TC, and inverse demand curves for a cable company in Berkeley would be:
TC = 2Q - 0.1Q2 + 0.005Q3 and
P = 20 - 0.5Q,
Where output Q is measured in thousands and P is the monthly basic tier price.
(You can directly use MC = 2- 0.2Q + 0.015Q2)
(a) Given this information, what are the equations for the total and marginal revenue curves?
(b) City Councilor A believes the city should own and operate a cable system for the purpose of making as much profit as possible. The profit would be used to lower the city government's deficit. If Councilor A gets her way, what will be the price and output of cable and by how much will the city-owned system be able to reduce the city's deficit? (Hint: consider the city as a government monopoly)
(c) Councilor B believes the city should produce as much cable service as possible without losing money (that is, the city should provide cable to its citizens on a nonprofit basis). If Councilor B gets his way, what output and price will result? (Hint: producer makes zero profit only when P = ATC)