1.   (22 pts) A monopolist has the long run cost function of C (Q ) =〈 where A > 0

Inverse market demand is PD (Q) = 130  2Q .

a.   Assuming no shut-down, find the monopolist’s profit maximizing price and quantity. (Each may be a function ofA.)

b.   Write down the inequality that must hold if the firm does not shut down. You do not need to simplify this equation. Briefly explain why the firm  uses this condition.

c.   Suppose the government uses a price ceiling in an attempt to achieve the efficient level of output in this market. What price ceiling should it use? Given this price ceiling, how does the range ofA under which the firm   does not shut down compare the range ofA for part (b)? Do not do any   additional calculations but provide a brief explanation.

2.   (22 pts) A monopolist serves two separate markets and has the long run cost function of C (Q) = 3Q +Q2  where Q = q1 + q2  . The firm can distinguish

between consumers in the two markets. Inverse demand in the first market is   equal to P1D (q1 ) = 80  q1 . Inverse demand in the second market is equal to      P2D (q2 ) = 80  4q2 . The monopolist can charge different prices in each market.

a.   Assuming no shut down find the monopolist’s profit maximizing prices and quantities in these two markets.

b.   Find the monopolist’s total profit.

c.   Suppose the monopolist gains access to a third market and is able to          charge a separate price in that market. In what direction will the                 monopolist’s profit change from your answer to (b). In what direction will total consumer surplus from the original two markets change? Briefly       explain your logic in each case.

3.   (22 pts) Two firms are competing by simultaneously choosing quantity in a         market. Both firms produce at zero cost. Firm 1 has the long run cost function of C (q1 ) = 0 and firm 2 has the long run cost function of C (q2 ) = 0 . Inverse market demand is PD (Q) = 60 - 3Q where Q = q1 + q2 .

a.   Assuming no shut-down, find the Cournot equilibrium quantity for each firm. Start from profit maximization.

b.   Calculate the market price and each firm’s profit.

c.   Suppose the two firms successfully collude. In what direction will total  profit change? In what direction will total consumer surplus change? Do not calculate anything but provide a brief, intuitive explanation.

4.   (22 pts) Exactly 5 firms are competing by simultaneously choosing quantity in a   market. Each of the first three has the long run cost function of Ci(qi) = 4qi . Each  of the remaining two has the long run cost function of Ci(qi) = 8qi . Inverse market demand is PD(Q) = 200 – Q where Q = q1 + q2 + q3 + q4 + q5 . Assume that no firm shuts down.

a.   Find the reaction function for each of the two types of firms.

b.   Calculate the Cournot equilibrium quantities and price.

c.   Suppose a sixth firm enters this market with the long run cost function of C6(q6) = 6qi . In what direction will each type of firm’s individual profit   change? Do not calculate anything but provide a brief, intuitive                explanation.