{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

468_ps3_2008_sol

# 468_ps3_2008_sol - ECON 468 Industrial Organization Problem...

This preview shows pages 1–3. Sign up to view the full content.

ECON 468: Industrial Organization Problem Set 3 April 24, 2008 1. Consider linear-city 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 two-period 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The two profit functions are given by: π 1 ( x ) = (3 t 2 + c - ( c - x )) 2 18 t π 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 0 < x , the best-response function shift down as we go from x 0 to x . Therefore the equilibrium price is decreasing in the level of investment. Similarly, the profits of firm 1 are increasing in x , while firm 2 ’s are decreasing in
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

468_ps3_2008_sol - ECON 468 Industrial Organization Problem...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online