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Economics 100C: Microeconomics C

Midterm 2

November 16, 2012

1. (22 pts) A monopolist sells a product in a market with exactly two consumers, a low demand individual and a high demand individual. The monopolist has a constant, long run, marginal cost function with MC = 20. The monopolist can offer menus of two-part tariffs. Each menu consists of a fixed fee, F and a per- unit price, p. As a part of the optimal set of menus, the per-unit price intended for the low demand individual is 40.

20/3

a. Determine the optimal set of menus. That is find F1, F2 and p2 . (p1 was given above.) Show your work or explain your logic.

b. Suppose that another low demand individual (identical to the original) enters this market. Determine the direction of change for the optimal set of menus, F1, p1, F2 and p2 . You do not need to do any calculations but you do need to explain your logic.

2. (30 pts) Two firms are competing by simultaneously choosing quantity in a market. Firm 1 has the long run cost function of C1 (q1 ) = 4q1(2) . Firm 2 has the

long run cost function of C2 (q2 ) = 5q2(2) . Inverse market demand is PD (Q ) = 123 - 2Q where Q = q1 + q2 .

a. Find the Cournot equilibrium quantity for each firm.

b. Find the Cournot equilibrium price.

c. Suppose firm 2’s cost function shifts up. That is, it becomes

C2 (q2 ) = (5 + a ) q2(2) where a > 0. Determine the direction of change for the equilibrium quantity for each firm and the equilibrium price. You do not need to do any calculations but you do need to explain your logic.

3. (26 pts) Exactly 5 firms are competing by simultaneously choosing quantity in a market. Each firm has the long run cost function of Ci(qi) = qi(2) . Inverse market demand is PD(Q) = 120 – Q where Q = q1 + q2 + q3 + q4 + q5 .

a. Find the reaction function for one of these firms.

b. Calculate the Cournot equilibrium quantities and price.

c. Suppose one of the firms exits the market. In what direction will price, the quantity produced by a single firm and overall market quantity change? You do not need to do any calculations but explain your logic.

4. (22 pts) Each of the graphs below is of the reaction functions for two firms who are competing by simultaneously choosing quantities (Cournot).

a. Illustrate the Cournot equilibrium quantities and sketch each firm’s iso- profit curves through this equilibrium.

b. Suppose that firm one chooses its quantity first. Firm 2 observes this quantity and then chooses its quantity (Stackelberg). Illustrate the Stackelberg equilibrium quantities and sketch each firm’s iso-profit curves through this equilibrium.

c. Suppose that firm two’s cost function shifts up. Illustrate how the equilibrium in part (b) will change. In which direction will each firm’s profit change? Give a brief, intuitive explanation.