Economics 111 - Principles of Economics - Accelerated Treatment - Problem Set 5
1. Suppose the price at which a monopolist can sell its product is P = 10 - Q, where Q is the number of units sold per period. The monopolist's MC = ATC = $4.
a) Graph the demand curve.
b) Graph total revenue for output levels from 0 to 10 units.
c) Graph the marginal revenue at each output level.
d) Which output level maximizes profit?
e) How much is maximum profit?
2. A monopolist of a new computer software is facing demand: P = 100 -2 Q (where P is the unit price for this software and Q is its quantity) and MC = 20.
a) What is the equilibrium quantity and price for this monopolist?
b) Graph the AR, MR, MC curves and equilibrium for this monopolist
c) What is the consumer surplus in this market?
d) How high is the deadweight loss in this market?
e) What is the monopolist's revenue and what is the monopolist's profit in this market?
3. A monopolist sells his product in two markets and no resale is possible. If the inverse demand curves in the two markets are: P1 = 200-X1, and P2 = 300 - X2 respectively, and the marginal cost is: MC = 2 (X1+X2).
a) What are the quantities the monopolist will sell in the two markets?
b) What is (are) the price(s) the monopolist will charge in the two markets?
4. You are given the market demand in a price leadership model: P = 600 - Q. You are also given the aggregate supply for all small firms in this industry P = 60 + Q and the marginal cost for the dominant firm: MC = 130.
a) Graph the market demand, small firm supply, MC, and dominant firm residual demand curves.
b) What is the equilibrium quantity the dominant firm will produce in the industry?
c) What is the price the dominant firm and the small firms will choose in this industry?
d) What is the aggregate quantity all small firms will produce jointly in this industry in equilibrium?
5. Firms A and B are two identical firms in a Cournot Duopoly. Assume that the market demand in this industry is given by P=100- (1/2) Q and marginal cost: MC = 50.
a) What is the quantity firm B will produce if Firm A were to produce zero quantity of the good?
b) What are the quantities firms A and B would produce respectively in a Cournot equilibrium?
c) Graph the reaction functions and show the Cournot equilibrium in your graph.