Question

Exercise 5 Let us consider a market where 4 firms compete à la Bertrand. The demand function is given by q() = 250 - 7p. The cost function is the same for both firms and it is C(q) = 100; for all i E {1,2,3,4} • Write explicitly the demand and profit functions of 1, 2, 3, and 4. • Derive best reply functions and the Nash equilibrium of the game. (9) = 591, what • If firm 1 find develop a new technology and produce at a new cost would happen in the market? • Find the discount factor that can sustain a collusive agreement where firms equally share the market if firm interact for 10 period. • What if they interact an infinite number of periods?

Answer 1

Answege :- Griven that:9CP) = 250 - 7P (192) - 1098 ie$ 1,2,3,43 Demand function of i q(P) - 250 - HP qi - 250 - 71 p250-qi i e$ 1,2,3,44 Profit function A(93) - P21 - 09i = (250-41 )?: - cqi i€{1,2,3,44 + fose best steply function derivate 1 (9i) w.8t qi dilli) 250 293 drí 77 Equating it equal to zero 7 (250) = Li 125 - 7 : BR (9) iE {1,2,3,42 Nosse Equilibrium is 34.750 T9 - 105-19

NADAL ③ Profit function of firm 1,19,) - P9,-6,19.) ; • 250.9.) 7.- 59. on grown ? mine ko 4 217 da, Putting dd,(9.).0 o aq word 291 - 9505 position -5) 125 - 35 250-35 - 215 Hinta whereas 92 - 98394,5125- while 9,5 195.35 If c for firm 2, 3, 4 is greater than 5 then output produced by them is lower than of firm 1 If for form 2, 3, 4 is less than 5 then output produced by them is greater than of firm in i

@ The discount factose(s) of profits is a sta misma ) For 10 Period T"+8+,*"+844*) + ..... 8°C 7m) = 4" (1+8+87 ..... 8°) 4 u 178.1) J Threshold of is in h - 14 = 3/4 * For infinite number of periods *" + 4 89" 46"a"..... MM (1+8+67.....) , , "(-4)