1. A monopoly faces demand given by Q = 200 -P. The marginal cost MC = $10 is constant. The marginal revenue MR = 200 -2Q.
a. Graphically show the monopoly's equilibrium.
b. What is the equilibrium price and quantity?
c. What are the profits earned by the monopolist?
d. Suppose the government forces the monopolist to behave like a competitive firm. What will be equilibrium price and quantity now? What will be the firm's profits?
2. A monopolist sells travel services to two groups of people with the following demand curves Q1 = 100 -2P1 (and MR1 = 50 -Q1) and Q2 = 60 -P2 (and MR2 = 60 -2Q2). The marginal cost of providing one unit of travel service to either of the groups is the same for the monopolist MC = $10 per unit.
a. Identify whether group 1 or group 2 has more elastic demand.
b. If the monopolist can price discriminate, what will be the prices at which he sells travel services to the two different groups. What will be the quantity sold to each group?
c. Suppose the monopolist isforced to charge a single price to all consumers regardless of the group to which they belong. What will be the new equilibrium prices and quantities? Who benefits from this policy? Who loses?
d. What would the equilibrium prices and quantities be if the market was competitive?
3. Suppose that a monopoly has a constant marginal cost (MC = $5) per unit of output produced. The monopolist sells its goods in two different markets that are separated by some distance. The demand curve in the first market is given by Q1 = 55 -P1 (and MR1 = 55 -2Q1) and for the second market by Q2 = 70 -2P2 (and MR2 = 35 -Q2).
a. If the monopolist can maintain the separation of the two markets, what will be equilibrium price and quantity in each market? What will be the monopolist'stotal profits?
b. Suppose that it costs demanders only $5 to transport goods between the two markets. How would your answer change about equilibrium prices and quantities in the two markets? What would be the monopolist's total profits in this situation?
c. Suppose transportation costs were zero and the monopolist was forced to follow a single-price policy. What would be the equilibrium prices and quantities now? What would be the monopolist's profits?