Question

4. (25 points) Suppose there are only two firms producing widgets. The total cost function for each firm is identical and is given by T℃(a = 8h, where gi is the output of firmi A market research company has found that demand for widgets can be described by the inverse demand function P 200 2Q, where Q-q (a) (10 points) A firm's action in the Courot Duopoly game is to choose an output level. Draw each firm's reaction function as a function of the other firms output Are there any strictly dominated actions in this game? (b) 7 points Find the Nash equrim of this game, e. the equilibrium the output produced by each firm Is the total output produced different from one that would be produced if the market was oated by a single monopolist (with the same cost function as the duopolists? (You should calculate the output produced by the monopolist in order to give a thorough answer) (c) (8 points) Now suppose there were ten firms instead of two. What will be the Nash equilibrium level of output that each firm produces in this case? What will be price in the market in this case? Is it different from the price in the case with two firms? Why or why not?

Answer 1

Gourmet Game → Ti-CP-Mc)9,-(Soo-29,-M2-89 a) Now 4 232 B total olp 8 64 Now 3n Monopoly,atn MB-MG 800 -48 8 192- 48M, 6 48 hus total olp undes Coumot Gome is higheor than totas ole Pradueea bur Monopolist 10 12-20- 82

4-181-4 192 28 =. 25-45 . Ans ouw with tuoo fom individuat frome hence Inice chasped fal due to ted Competiton

100 (0, 96) BR of first firm (0, 48) 50 cournot nash eqm 32, 32) BR of 2nd firm (48, 0) ( ) 96. 0 0 Quantity of1