Lecture8寡头IIIBertrand.ppt

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EC 3322 (Industrial Organization I) EC 3322 (Industrial Organization I) * Lecture 8: Bertrand (Price) Competition * Introduction In a wide variety of markets firms compete in prices In monopoly, setting price or quantity first makes no difference But, in oligopoly the strategic variable matters a great deal ? price competition is much more aggressive than quantity competition * Bertrand Competition In the Cournot model price is set by some market clearing mechanism An alternative approach is to assume that firms compete in prices ? it leads to dramatically different results Take a simple example two firms producing (or selling) an identical product (mineral water or fruits) firms choose the prices at which they sell their products each firm has constant marginal cost of c inverse demand is P = A – B.Q direct demand is Q = a – bP with a = A/B and b= 1/B EC 3322 (Industrial Organization I) * Bertrand Competition We need the derived demand for each firm ? demand conditional upon the price charged by the other firm Take firm 2. Assume that firm 1 has set a price of p1 if firm 2 sets a price greater than p1 she will sell nothing if firm 2 sets a price less than p1 she gets the whole market if firm 2 sets a price of exactly p1 consumers are indifferent between the two firms: the market is shared, presumably 50:50 So we have the derived demand for firm 2 q2 = 0 if p2 p1 q2 = (a – bp2)/2 if p2 = p1 q2 = a – bp2 if p2 p1 * Bertrand Competition This can be illustrated as follows: Demand is discontinuous p2 q2 p1 a a - bp1 (a - bp1)/2 There is a jump at p2 = p1 The discontinuity in demand carries over to profit * Bertrand Competition Firm 2’s profit is: Π2(p1,, p2) = 0 if p2 p1 Π2(p1,, p2) = (p2 - c)(a - bp2) if p2 p1 Π2(p1,, p2) = (p2 - c)(a - bp2)/2 if p2 = p1 Clearly this depends on p1. Suppose first that firm 1 sets a “very high” price: greater than the monopoly price of pM = (a +bc)/2b For whatever reason! * Bertrand Compet

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