7 Monopoly Practices Ch 14

7 Monopoly Practices Ch 14 - 4/2/2008 Chapter 14 Monopoly...

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4/2/2008 1 Chapter 14 Monopoly Practices and Price Discrimination Perfect Price Discrimination All price discrimination schemes share an underlying strategy to segment the market and to charge each segment a different price relative to its cost. Perfect Price Discrimination occurs when the monopolist can successfully extract the maximum possible profit from each customer and therefore the whole market. The monopolist knows exactly what each customer’s reservation price is (the most the customer is willing to pay). He charges each customer a price exactly equal to their reservation price. There is no consumer surplus because every customer pays exactly their willingness-to-pay price. This is hard to do in practice. A close example is an accountant who charges each client a different price.
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4/2/2008 2 Ordinary Price Discrimination More commonly, a monopolist is able to segment the market and allocate output and charge prices that will maximize the firm’s profit. A firm could segment by region, age, gender etc. The monopolist would have to know the demand (and hence, MR) in each market segment. A profit maximizing monopolist engaging in ordinary price discrimination will choose an aggregate output where (aggregate)MR=MC. Output is allocated so MR is the same in all market segments. Here’s the proof: For given supply levels y 1 and y 2 the firm’s profit is The profit-maximization conditions are Π ( , ) ( ) ( ) ( ). y y p y y p y y c y y 1 2 1 1 1 2 2 2 1 2 = + - + ( 29 29 29 Π y y p y y c y y y y y y y 1 1 1 1 1 1 2 1 2 1 2 1 0 = - + + + + + + × + + + = ( ) ( ) ( ) ( ) ( 29 29 29 Π y y p y y c y y y y y y y 2 2 2 2 2 1 2 1 2 1 2 2 0 = - + + + + + + × + + + = ( ) ( ) ( ) ( )
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4/2/2008 3 and so The profit-maximizing conditions are (MR 1 ) (MC) (MR 2 ) (MC) ( ) y y y 1 2 1 1 + = ( ) y y y 1 2 2 1 + + + = ( 29 29 29 y p y y c y y y y 1 1 1 1 1 2 1 2 ( ) ( ) ( ) = + + + + + + ( 29 29 29 y p y y c y y y y 2 2 2 2 1 2 1 2 ( ) ( ) ( ) . = + + + + + + In other words, MR 1 (y 1 *) = MR 2 (y 2 *) = MC is the profit-maximizing allocation of total output y = y 1 + y 2
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4/2/2008 4 Numerical Example p b = 36 – ½(30) = 21
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4/2/2008 5
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4/2/2008 6 Note that if you left numbers as decimals instead of converting to fractions, you would have found that profit equals $1934.58. On a test, don’t bother to convert to fractions. Note that the price is higher in the market where demand is more inelastic . Recall: MR(y) = P [1 – 1/|E|] Since the monopolist equates the MR across the different markets MR (y 1 ) = MR (y 2 ) p 1 [1 – 1/|E|] = p 2 [1 – 1/|E|] If the elasticities were equal then, p 1 = p 2 Suppose the elasticity of demand in market 2 was less elastic (more inelastic) than in market 1.
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4/2/2008 7 Then |E| in market 2 < |E| in market 1 1/|E| > 1/|E| [1 – 1/|E|] < [1 – 1/|E|]
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This note was uploaded on 06/18/2011 for the course ECON 2X03 taught by Professor Jamesbruce during the Fall '10 term at McMaster University.

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7 Monopoly Practices Ch 14 - 4/2/2008 Chapter 14 Monopoly...

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