Question

Economics 302: Intermediate Microeconomics II Assignment 3 (Due in my office 3:00, Thursday March 19) 1. Consider two firms, 1 and 2, each producing an identical good simultaneously. This good market demand given by the (inverse demand function p = 10 - Y, where p is price, and Y = 1 + y2 is market quantity. Vi represents the amount produced by firm i. These firms have cost functions as follows: Ci = Gyi, where ci = c = 1. (60 pts) a) Solve algebraically for these firm's reaction functions, expressing each firm's optimal output level given some level of its competitor's output. b) Graph these reaction functions and show the equilibrium point. Include isoprofit contours through the equilibrium point for both firms. c) Solve algebraically for the equilibrium: Determine the equilibrium market price, as well as each firm's equilibrium quantity and profit. d) Is your answer to part c) the only equilibrium possible? Explain.

Please include the graph!

Answer 1

40, DATE PAGE to P = 10-4 where y = y + y2 - ciye = yi Hi=1,2 firm i maremines to profit AL T = (10-41-42) y - a a (10-yl-yz) y - ys dal = 10-241 - 42 -1 0 - 9-42 = yo - 0 similarly i łz = (10-91-42) y 2 - y2 firm's reaction function 10 - 41 - 242 +_20 ③ о firma's reaction лады. - 9.41 = y a Cusskihakira o б ил 9- (9-4) - 241 18-9 +41 = 4yr 9 = 34s By symmemy y2 = 3 point of 4.5 RC2 9 g

DATE. PAGE 9 Already solved for equilibrium in part a. equilibrium price, p = 10-4 - 10-3-3 p=4 * = 4 x 3 - 3 łazy = 4x3-3 = 9
d) There is only one equilibrium.