MANAGERIAL ECONOMICS

Homework #2 - Oligopoly and Game Theory

The homework should be written on 8 1/2 by 11 paper. If you use paper torn out of a notebook, trim the ragged edges before you turn in your assignment. When calculations are required, you must show all work. If no work is shown, no credit will be given. The homework is due at the beginning of class on Tuesday, April 14.  No late homework will be accepted.  Please make a copy of your homework before you turn it in.

1.  Suppose the market demand for a product is given below:

Q = 40 - 2 P

There are four firms in the market and their marginal cost is equal to zero.  According to the Cournot model, how much should each firm produce?  What is the equilibrium price in this market?

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2.  Suppose a firm has the following demand curve for its product:

Q = 180 - 3 P

a.  If MC = 20 + 10 Q, what is the profit maximizing level of output and price for this firm?

b.  What would be the output and price if the firm wanted to maximize revenue instead of profit?

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3.  Consider the situation of an industry with a single incumbent firm but also a potential entrant to the industry. The entrant is trying to decide whether or not to enter the market and plans on matching whatever price the incumbent charges.  The incumbent firm is currently charging $50 for the product, but it has the option to lower the price to $30.  The payoff matrix to each firm in terms of profit made is given below:

a. If both firms make their decisions simultaneously, what will be the outcome in this market? Assume that this is a one-time action and the goal of each firm is to maximize its profits in the short-run.

b. Suppose the incumbent firm can make its decision on price before the other firm decides to enter. Use a game tree to determine what the incumbent firm should do. What will be the outcome in this case?