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

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Chapter 15 Imperfect Competition

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Short-Run Decisions: Pricing & Output 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?
Short-Run Decisions: Pricing & Output 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
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 j / q i = 0 for all j i
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
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 - - =
Natural Springs Duopoly The Nash equilibrium will be 1 2 2

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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 BR 1 ( q 2 ) 2 c a - 2 c a - 3 c a - 3 c a -
Cournot Best-Response Diagrams q 1 q 2

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