bertrand

bertrand - Price Competition: Bertrand In the Cournot model...

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ECO 171 Industrial Organization Price Competition: Bertrand • In the Cournot model price is set by some market clearing mechanism • Firms seem relatively passive • 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 water – each firm has constant marginal cost of $10 – market demand is Q = 100 - 2P Check that with this demand and these costs the monopoly price is $30 and quantity is 40 units
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ECO 171 Industrial Organization Bertrand competition (cont.) • 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 $25 – if firm 2 sets a price greater than $25 she will sell nothing – if firm 2 sets a price less than $25 she gets the whole market – if firm 2 sets a price of exactly $25 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 = $25 2 = 100 - 2p 2 if p 2 < p 1 = $25 2 = 0.5(100 - 50) = 25 if p 2 = p 1 = $25
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bertrand - Price Competition: Bertrand In the Cournot model...

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