11-Price Competition

# 11-Price Competition - Price Competition 1 Introduction In...

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Price Competition 1

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In a wide variety of markets firms compete in prices Internet access Restaurants Consultants Financial services With monopoly setting price or quantity first makes no difference In oligopoly it matters a great deal nature of price competition is much more aggressive the quantity competition 2 Introduction
In the Cournot model price is set by some market clearing mechanism An alternative approach is to assume that firms compete in prices : this is the approach taken by Bertrand Leads to dramatically different results Take a simple example two firms producing an identical product (spring water) 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 b.P with a = A/B and b= 1 /B 3 Price Competition: Bertrand

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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 p 1 if firm 2 sets a price greater than p 1 she will sell nothing if firm 2 sets a price less than p 1 she gets the whole market if firm 2 sets a price of exactly p 1 consumers are indifferent between the two firms: the market is shared, presumably 50:50 So we have the derived demand for firm 2 q 2 = 0 if p 2 > p 1 q 2 = ( a – bp 2 )/2 if p 2 = p 1 q 2 = a – bp 2 if p 2 < p 1 4 Bertrand competition
This can be illustrated as follows: 5 Bertrand competition Demand is discontinuous p 2 q 2 p 1 a a - bp 1 ( a - bp 1 )/2 There is a jump at p 2 = p 1 The discontinuity in demand carries over to profit

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6 Bertrand competition Firm 2’s profit is: 2 (p 1, , p 2 ) = 0 if p 2 > p 1 2 (p 1, , p 2 ) = (p 2 - c)(a - bp 2 ) if p 2 < p 1 2 (p 1, , p 2 ) = (p 2 - c)(a - bp 2 )/2 if p 2 = p 1 Clearly this depends on p 1 . Suppose first that firm 1 sets a “very high” price: greater than the monopoly price of p M = (a +bc)/2b For whatever reason!
7 Bertrand competition With p 1 > (a + bc)/2b, Firm 2’s profit looks like this: Firm 2’s Price Firm 2’s Profit c (a+bc)/2b p 1 p 2 < p 1 p 2 = p 1 p 2 > p 1 What price should firm 2 set? The monopoly price What if firm 1 prices at (a + bc)/2b? So firm 2 should just undercut p 1 a bit and get almost all the monopoly profit Firm 2 will only earn a positive profit by cutting its price to (a + bc)/2b or less At p 2 = p 1 firm 2 gets half of the monopoly profit

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8 Bertrand competition Now suppose that firm 1 sets a price less than (a + bc)/2b Firm 2’s Price Firm 2’s Profit c (a+bc)/2b p 1 p 2 < p 1 p 2 = p 1 p 2 > p 1 Firm 2’s profit looks like this: What price should firm 2 set now? As long as p 1 > c, Firm 2 should aim just to undercut firm 1 What if firm 1 prices at c?
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