Which situation is better for consumers?
1. The market demand for a good is represented by P = 400 20Q. Firms are symmetric with cost functions C = 30q. Assume the firms compete in a Cournot Oligopoly (i.e., simultaneous choices of quantity).
(a) Say there are two firms in the market. Solve for equilibrium production levels and prices.
(b) Now do the same for three firms.
(c) Which situation is better for consumers?
(d) Compute prices quantities, and consumer surplus under perfect competition in which each firm in the market takes price as a given.
(e) Now, think of a case where there are N firms. What are equilibrium prices and quantities, and how do they depend on N? As N rises, what happens to consumer surplus? [Hint: compare to your response in part d].
(f) Consider the same demand and cost functions from above, focusing on the case where there are two firms in the market. Suppose the two duopolists agree to a cartel in which they each produce half of the monopoly output. Show that this cannot be an equilibrium. [Hint: what is the best response of one firm if the other produces half of the monopoly output?]
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