Question

A book publisher faces two different markets with different price elasticities of demand for its books. In market A the price elasticity of demand is 5 and in market B the elasticity is 1.5. If the marginal cost of producing a book is $10, how should the firm price its books in the two markets? (2 points) Hint: Use Lerner Index. ?(1− 1/ ? ) = ?C

Answer 1

Relationship among price, MC and price elasticity of demand.

According to Lerner index:

P (1 - 1/e) = MC

Where 'e' is absolute value of price elasticity of demand.

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Market A

Price elasticity of demand (e) = 5

MC = 10

Use Lerner index:

P (1 - 1/e) = MC
=> P (1 - 1/5) = 10

=> P (1 -0.2) = 10

=> 0.8P = 10

=> P = (10/0.8)

=>P = 12.5

Firm should charge a price of $12.5 in Market A.

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Market B

Price elasticity of demand (e) = 1.5

MC = 10

Use Lerner index:

P (1 - 1/e) = MC
=> P (1 - 1/1.5) = 10

=> P (1 -0.67) = 10

=> 0.33P = 10

=> P = (10 / 0.33)

=>P = 30.3

=> P = 30

Firm should charge a price of $30 in Market B