ch15 - Chapter 15 Imperfect Competition Short-Run...

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Chapter 15 Imperfect Competition
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When there are only a few firms in a market, predicting output and price can be difficult how aggressively do firms compete? how much information do firms have about rivals? how often do firms interact?
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Bertrand model two identical firms choosing prices simultaneously for identical products end up with situation similar to perfect competition Cournot model firms set quantities rather than prices end up with a result between the Bertrand and the cartel models Cartel model firms act as a group end up with the monopoly outcome
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Bertrand Model Two identical firms producing identical products at a constant MC = c • Firms choose prices p 1 and p 2 simultaneously single period of competition All sales go to the firm with the lowest price – sales are split evenly if p 1 = p 2 • The only pure-strategy Nash equilibrium is p 1 * = p 2 * = c both firms are playing a best response to each other neither firm has an incentive to deviate to some other strategy
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Nash Equilibrium of the Bertrand Model • If p 1 and p 2 > c , a firm could gain by undercutting the price of the other and capturing all the market • If p 1 and p 2 < c , profit would be negative The same result will arise for any number of firms n 2 The Nash equilibrium of the n -firm Bertrand game is p 1 * = p 2 * = … = p n * = c The Nash equilibrium of the Bertrand model is identical to the perfectly competitive outcome It is paradoxical that competition between as few as two firms would be so tough
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Cournot Model • Each firm chooses its output q i of an identical product simultaneously • Total industry output Q = q 1 + q 2 +…+ q n determines the market price P ( Q ) P ( Q ) is the inverse demand curve corresponding to the market demand curveEach firm recognizes that its own decisions about q i affect price P / q i 0 However, each firm believes that its decisions do not affect those of any other firm q / q = 0 for all j i
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Cournot Model The FOC for profit maximization are ( 29 ( 29 0 ) ( ' ' = - + = π i i i i i q C q Q P Q P q • The firm maximizes profit where MR i = MC i
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Natural Springs Duopoly Assume that there are two owners of natural springs – firm’s cost of pumping and bottling q i liters is C i ( q i ) = cq i each firm has to decide how much water to supply to the market The inverse demand function is P ( Q ) = a – Q
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Natural Springs Duopoly In the Bertrand game the two firms set price equal to marginal cost P * = c total output = Q * = a – c
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Natural Springs Duopoly The solution for the Cournot model is similar 2 2 1 c q a q - - = 2 1 2 c q a q - - =
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Natural Springs Duopoly The Nash equilibrium will be
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Cournot Best-Response Diagrams q 1 q 2 a - c The intersection of the firms’ best- response functions is the Nash equilibrium a - c 1 2 2 c a - 2 c a - 3 c a - 3 c a -
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ch15 - Chapter 15 Imperfect Competition Short-Run...

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