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Unformatted text preview: in scope because it does not consider the possibility of new firms entering the industry. 3. The assumption that firms take each other's output as given and do not learn from past experiences is nave. 285 4. The model focuses exclusively on quantity competition, with no attention paid to price competition whatsoever. 5. It is difficult to believe that a small number of firms would not collude against consumers in one way or another. Let's consider a Cournot Duopoly Quantity competition in a simultaneous game theory setting. Consider 2 firms, firm A and B, producing identical products so that they are forced to charge the same price. This leaves the sole strategic choice as the amount the firms choose to produce, QA and QB. Once the firms select their quantities, the resulting price is whatever price is required to "clear the market". This is the price where consumers are willing to buy QA + QB (the total production). Suppose the firms have no marginal cost of production (for now). Let the market demand be given by: where, QA + QB = QTOTAL QA + QB = 600 P Now, we are interested in price so we rewrite market demand as: P = 600 - QA - QB If these firms make their output decisions simultaneously, how much will each firm produce? To reach an equilibrium, both firms must be choosing the output level that is a "best response" to the choice of the other firm. Consider the output decision of Firm A. For QA to be an equilibrium output for firm A, it needs to maximize profits for firm A given firm B's choice, QB. So, suppose that firm A believes that firm B is going to produce QB. Then firm A estimates that if it produces QA units of output its profit will be: A = P QA which is, A = (600 - QA - QB) QA A = 600QA - QA2 - QAQB To maximize this profit function we need to take the partial of with respect to QA and set the resulting expression equal to zero (i.e. marginal profit =0). 286 FOCQA 600 QB - 2QA = 0 2QA = 600 QB QA = 300 0.5QB (1) This profit maximizing output equation for QA is called firm A's best response to firm B (firm A's reaction function). We should...
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- Spring '10