Suppose there are n firms in a Cournot oligopoly model. Let q_i denote the quantity produced by firm i, and let Q =q₁ + q₂ +...+ q_n 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 q_iis C(q_i) = cq_i . 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?