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Consider a cournot market model with three firms. The market demand (inverse) curve is P(Q) = a – Q , where Q = q1 + q2 + q3 and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c, no fixed cost. Find the equilibrium quantities, price and profits for the firms. Now consider that (i) firm 1 chooses q1 >= 0 and (ii) firm 2 and firm 3 observe q1 and then simultaneously choose q2 and q3, respectively. Find the new equilibrium quantities, price and profits for the firms and compare the result with the previous situation.
(source : gibbons)
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