Problem
(The n-Firm Cournot Model) Suppose there are n 2 2 firms in the Cournot oligopoly model. Let qi denote the quantity produced by firm i, and let Q = q1 + + qn denote the aggregate production level. Let P(Q) denote the market price (when demand equals Q) and assume that demand function is given by P (Q) = a-Q (where Q?a). Assume that firms have no fixed cost, and the cost of producing quantity qi is c . qi (all firms have the same marginal cost c, and assume that Q < a).
a. If we model firms' production decisions as a static game with complete information, can you show the normal-form representation of this game?
b. What is the Nash Equilibrium of the game where firms choose their quantities simultaneously?
c. What happens to the equilibrium price as n approaches infinity? Is this familiar?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.