468_ps2_sol - ECON 468 Industrial Organization Solution to...

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Unformatted text preview: ECON 468: Industrial Organization Solution to Problem Set 2 March 18, 2008 1. Consider a set of 3 identical firms i = 1 , 2 , 3 with cost function C i = 10 Q i participating in a market for homogeneous products with demand Q = 100- P where Q = Q 1 + Q 2 + Q 3 . Assume that firms compete by choosing the QUANTITIES they produce. (a) Assume that firms interact only once. Find how much each firm produces in the unique Nash (Cournot) equilibrium of this game. What is the price and the profits of each firm? For each firm i , the reaction functions are given by: R i ( Q- i ) = 45- 1 / 2 Q- i . Imposing the symmetry of the solution (i.e. q 1 = q 2 = q 3 ), the equilibrium outcomes are given by: q c = 45 / 2 p c = 65 / 2 π c = 45 2 / 4 (b) Assume now that firms 2 and 3 merge. The market now includes firm 1 and the new entity 2 . Compute the new equilibrium outcomes of the quantity-setting game (i.e. quantities, price, and profits). The modified reaction functions are given by: R 1 ( q 2 ) = 45- 1 / 2 q 2 , R 2 ( q 1 ) = 45- 1 / 2 q 1 . The equilibrium outcomes become: q c 1 = q c 2 = 30 1 p c = 40 π c 1 = 30 2 π c 2 = 30 2 (c) What is the impact of the merger on consumers’ surplus and firms’ profit? Are firm 2 and firm 3 benifiting from the merger? What about firm 1? Consumer surplus is equal to: CS = (100- p ) Q ( q ) 2 . Using the solution to ?? and ?? , the change in consumers’ surplus due to the merger is: CS c- CS c = 60 2 2- 135 2 8 =- 478 . 125 . Therefore, consumers are loosing from the merger. The change in profits to firm 1 due to the merger is given by: π c 1- π c 1 = 30 2- 45 2 4 = 393 . 75 π c 2- ( π c 2 + π c 3 ) = 30 2- 45 2 2 =- 112 . 5 Therefore, firm 1 is gaining from the merger of 2 and 3 . On the other hand, the new entity is earning a smaller profit than before. (d) Assume now that the merger between firms 2 and 3 generates a reduction in the marginal cost of production. In particular C 2 ( Q ) = ω 10 Q , where ω ∈ (0 , 1]. Compute the new equilibrium outcomes of the quantity-setting game (i.e. quantities, price, and profits). If C 2 ( Q ) = ω 10 Q , the reaction functions are given by: R 1 ( q 2 ) = 45- 1 / 2 q 2 , R 2 ( q 1 ) = 100- 10 ω 2- 1 / 2 q 2 . The equilibrium outcomes are given by: p c 00 = 110 + 10 ω 3 q c 00 1 = 80 + 10 ω 3 2 q c 00 2 = 110- 20 ω 3 π c 00 1 = (80 + 10 ω ) 2 9 π c 00 2 = (110- 20 ω ) 2 9 (e) What is the minimum level of cost reductions ω necessary to make the merger between 2 and 3 profitable (i.e. π c 2 ( c = 10 ω ) > π 1 ( c = 10) + π 2 ( c = 10))?...
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This note was uploaded on 08/08/2008 for the course ECON 468 taught by Professor Houde during the Spring '08 term at University of Wisconsin.

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468_ps2_sol - ECON 468 Industrial Organization Solution to...

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