This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECON 468: Industrial Organization Problem Set 3 April 24, 2008 1. Consider linearcity market in which 2 firms are located at the opposite end of the line: Figure 1: Linear city with two stores G 1 and G 2 G 1 = 0 x G 2 = 1 We know that in this market the demand functions at each store are given by: D 1 ( p 1 ,p 2 ) = p 2 p 1 2 t + t 2 D 2 ( p 1 ,p 2 ) = p 1 p 2 2 t + t 2 Consider the following twoperiod game: In period 1, Firm 1 can reduce its marginal cost by investing in research and development. In period 2, both firms compete in prices (i.e. Bertrand game with product differentita tion). The cost function of the two firms is given by: C 1 ( q ) = ( c x ) q C 2 ( q ) = cq where x is the result of the investment made in period one. The cost of reducing marginal cost by x is given by: g ( x ) = 1 2 x . (a) Given an arbibtrary value for x , what are the equilibrium profits of both firms in the second stage of the game? 1 The two profit functions are given by: 1 ( x ) = (3 t 2 + c ( c x )) 2 18 t 2 ( x ) = (3 t 2 + ( c x ) c ) 2 18 t (b) Draw the reaction functions of both firms for two values of x . In which direction are equilibrium prices changing when we increase the amount of investment x ? What about profits? The reaction functions are given by: R 1 ( p 2 ) = t 2 + c x 2 + p 2 2 R 2 ( p 1 ) = t 2 + c 2 + p 1 2 If we evaluate R 1 ( p 2 ) at x < x , the bestresponse function shift down as we go from x to x . Therefore the equilibrium price is decreasing in the level of investment. Similarly,....
View
Full
Document
This note was uploaded on 08/08/2008 for the course ECON 468 taught by Professor Houde during the Spring '08 term at Wisconsin.
 Spring '08
 HOUDE
 Perfect Competition

Click to edit the document details