A market is characterized by a demand curve that can be expressed as P = 96 – (1

Question

A market is characterized by a demand curve that can be expressed as P = 96 – (1/3) Q. Each of the firms currently serving the market has a total cost function of the form C = 12 q so MC = ATC = 12. There are no fixed costs.

a. If the market is served by numerous perfectly competitive firms, calculate the equilibrium P* and Q*. Show work. If the market is served by a profit-maximizing monopolist, calculate monopoly P* and Q* in the market. Show work.

b. If the market is served by a monopolistic firm that practices limit pricing, find P* and Q* for the limit-pricing monopolist, assuming that each potential entrant has the total cost function given by C = 35 q. Show work.  If the market is served by two symmetric Cournot duopolists, find P* and Q* for the duopoly market. Show work.

c. On a piece of graph paper, plot the market demand curve. Then, plot and label 4 (Q*,P*) combinations on the demand curve: for perfect competition, monopoly, limit-pricing monopoly, and duopoly market. Note: there are a number of sites that have graph paper for downloading, e.g., http://www.math.kent.edu/~white/graphpaper/.

Explanation / Answer

a. For both the markets, optimal output is where MR = MC

96-2/3Q = 12

Q = 126.

In perfect competition, profit maximization P=MR=MC = 12.

In monopoly, substitute Q value in demand equation. 96 - (1/3)*126 = P

54 is the monopoly price.

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