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ImperfectComp1

# ImperfectComp1 - Short-Run Decisions Pricing Output When...

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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? The difficulty arises b/c of the strategic interaction. Hence, we have to use (or get to use, depending on your perspective) game theory…

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Short-Run Decisions: Pricing & Output Begin by considering two extremes Perfect competition Monopoly Price P ** Quantity MC=AC Q * P * Q ** D MR
Short-Run Decisions: Pricing & Output Why should we care? Price It is important to know where the industry ends up because total welfare depends on price and quantity Under perfect competition, there is no DWL P ** The monopoly Quantity MC=AC Q * P * Q ** D MR implies a DWL

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Bertrand Model: With undifferentiated goods 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 Although this is a continuous game (remember game theory?), we can’t solve it using calculus (unlike the tragedy of the commons) because payoffs are not continuous.
Nash Equilibrium of the Bertrand Model The only pure-strategy Nash equilibrium is p 1 * = p 2 * = c Both firms are playing a best response to each other: If either firm raises its price, it sells nothing (and its profit doesn’t change), so this is an equilibrium Does another pure-strategy NE exist? Suppose p 1 and p 2 > c and p 1 = p 2 Suppose p 1 and p 2 > c and p 1 > p 2 (and vice versa) Suppose p 1 > c and p 2 = c (and vice versa) Suppose either price less than c

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Nash Equilibrium of the Bertrand Model The same result will arise for any number of firms n 2 if costs are identical The Nash equilibrium of the n -firm Bertrand game is p 1 * = p 2 * = … = p n * = c What if there are n 2firms with different constant marginal costs? First, consider: c 1 < c 2 < c 3 < …< c a Second, consider c 1 = c 2 ≤ c 3 ≤ … ≤ c a
Bertrand Paradox The Nash equilibrium of the (equal and constant marginal cost) Bertrand model is identical to the perfectly competitive outcome It is paradoxical that competition between as few as two firms would be so tough We’ll see later that we can continue to assume price competition (i.e. Bertrand competition) and get rid of this paradox.

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CournotModel In the Bertrand model, each firm chooses the price at which it will sell its goods. In the Cournotmodel firms choose quantities to supply to the market. Each firm chooses its output q of an identical i 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 curve
CournotModel Each firm recognizes that its own decisions about q i affects price P / q i 0 However, each firm believes that its decision

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