Question

6. Price competition in simultaneous move differentiated product duopoly: There are only two gourmet food restaurants in a town. Their menus are not identical, but not totally different either. The price for each entree in a restaurant is the same. The restaurants pick their prices and sell according to their demand. The demand curve faced by restaurant 1 is given by: = 100 – 4p1 + 2p2 and by restaurant 2 is given by: y= 100 – 4p2 + 2p1. The costs are C1(x) = 5x and C (y) = y, where firm 1 serves a consumers and firm 2 serves y consumers. (a) Determine the reaction function for each firm. (b) How much output will each firm produce in equilibrium? At what price? How much will be the equilibrium profit for each firm?

Answer 1

(a) Ti = P. a- ci(x) = Pixe - 5% =(P1-5) = ( -5) C100-4 Pi + 2P2) 8IT, = (100-UP,+2P2) (1-0) + (P1 - 5)(-4) = 10o-upit 2P2 -up, +20 = 120 - 8 Pi +2P2 - put o =0 732 120-8P1+2P2 120 + 2 P2 ao = 8P, 120 + 2/2 = Pi - 15+ P2 =P BRI : P = 15+ P2 1 = - P2Y - (219) P2Y - 25 y = (Pq - 25g = ( P2 – 2574100 - 482 + 28,).

02 = 100 - ५९ + 282 11-02 + (P2- 25/0-५+0) = 100-42 - 281 - ५१2 + 50 __= 150 - 822 + २१ put all to 150 - 882 + 28, 20 150 + 281 = 82 ___ 18.35 + १ = ka ___BK : 2 = 18.15 + b)__2 =_28. 35 +4 15 + 4) __ - 18. +5 + 3.75 + 2 _ 2 _= 2 - 22. 5 - = 22.5 = 22.5 1582 82 = 16x 225 2 - 24

P, = 15 29 6 f, = 21 x= = 100 -4P,72P2 2 съ - ч (21) + 2(29) = Поъ – 84 + 98 - 69 9 = 9 = 200 — чP. + 2, 200 - 9 (29) +2 (21) = 160 - 96 + 42 = 96 Т, Е = Рік- 52 (е, -52 = (2) - 52 69 = 16x49 = 102 9 T, = P - 259 = (fa - 2 ) - | 24 – 25) 96 = = = 129 – 12.5) че 1.5 х 4 529