Microeconomics

3. Oligopoly A monopolist can produce at a constant average (and marginal) cost of AC = MC = $5. It faces a market demand curve given by Q = 53 p. (a) (b) (f) (g) Calculate the protmaximizing price and quantity for this monopolist. Also calculate its prots. Suppose a second rm enters the market. Let (11 be the output of the rst rm and (1;; be the output of the second. Market demand is now given by (11 + (12 = 53 p. Assuming that this second rm has the same costs as the rst, write the prots of each rm as functions of ql and q2. Suppose (as in the Cournot model) that each rm chooses its prot-maximizing level of output on the assumption that its competitor's output is xed. Find each rm's reaction curve (i.e., the rule that gives its desired output in terms of its competitor's output). Calculate the Cournot equilibrium (i.e., the values of ql and q2 for which each rm is doing as well as it can given its competitor's output). What are the resulting market price and prots of each rm? Suppose there are n rms in the industry, all with the same constant marginal cost, MC = $5. Find the Cournot equilibrium. How much will each rm produce, what will be the market price, and how much prot will each rm earn? Also, show that as 71 becomes large, the market price approaches the price that would prevail under perfect competition. Assume that n = 2. Suppose Firm 1 is a Stackelberg leader (i.e., makes its output decisions before Firm 2). Find the reaction curves that tell each rm how much to produce in terms of the output of its competitor. How much will each rm produce, and what will its prot be