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Suppose there are n firms in a Cournot oligopoly model. Let qidenote the quantity produced by...

Suppose there are n firms in a Cournot oligopoly model. Let qidenote the quantity produced by firm i, and let Q = q1 + q2 +…+ qn be the aggregate quantity in the market. Let P denote the market clearing price and assume that the inverse market demand is given by P(Q)=a - Q (when Q<a, else P=0). Assume that the total cost for firm i of producing quantity qi is C(qi) = cqi . That is, there are no fixed costs and the marginal cost is constant at c, where we assume c < a. Following Cournot, suppose that the firms choose their quantities simultaneously. What is the Nash equilibrium? What happens as n approaches infinity?

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