review questions_ak part2.pdf

# Using demand functions we derived above we solve the

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Using demand functions we derived above, we solve the Bertrand-Nash equilibrium. Firm 1°s prob- lem is to maximize p 1 D 1 ( p 1 ; p 2 ) = p 1 2 ° p 1 + p 2 2 The FOC is 2 + p 2 2 ° p 1 = 0 : The FOC of ±rm 2°s problem is p 2 ° p 2 2 ° p 1 + p 2 2 1 ° 2 ° p 1 2 ° p 2 = 0 : Using these reaction functions, we solve for p 1 p ° 1 = 4 3 ; and so p ° 2 = 2 3 : Then, pro±ts are 1 = 8 9 2 = 2 9 : (c) What are market shares in equilibrium? Since D 1 ( p ° 1 ; p ° 2 ) = 2 3 and D 2 ( p ° 1 ; p ° 2 ) = 1 3 ; the market shares for shop 1 and shop 2 are 67% and 33%, respectively. 11. Staples and O¢ ce Depot tried to merge their o¢ ce-supplies superstore chains in 1996. Under which of the following market de°nitions, is this merger proposal most likely to be approved? (a) A relevant market is ²market of all stores selling all non-food products³ (b) A relevant market is ²market of all stores selling o¢ ce supplies³ 4

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(c) A relevant market is ²market of o¢ ce-supplies superstores³ In reality, this merger plan was not approved. What was the main reason behind this decision of the FTC? Under market de±nition (a), the aggregate market share of Staples and O¢ ce Depot would be smallest. Therefore, under market de±nition (a), the proposed merger would be most likely to be approved. For the reason behind the decision, see pages 9 and 10 of Lecture 3 lecture notes. 5

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