Microeconomics - Game Theory and Oligopoly

Problem 3 Oligopoly - A Cournot Game Solved in Recitation Consider the market for lysine, a protein. The market demand for lysine is Qd = 70 P. Firms in the lysine market have total cost equal to TC(q) = 200 + qu. Suppose the entire market for lysine is controlled by one monopolist. Suppose also that the rm cannot prevent re-sales and charges the same price to all buyers on all units. a) Find the monopolist's prot maximizing quantity and price. b) Find the consumer surplus and the monopolist's prot (Le, Revenue TC) when the monopolist maximizes prot. c) What is the unit cost of lysine? Now, suppose that after winning an anti-trust law suit the government breaks the monopolist into two separate rms, Chem One and Chem Two. Each firm would still have total cost TC = 200 + qu. In the lysine industry, building capacity takes time and the two firms compete by choosing capacity level. Each firm must commit to a capacity expansion or reduction plan before learning the details of its competitor's plan. The two rms are prot maximizers. d) Describe Chem One's and Chem Two's strategic interaction as a game in normal form. e) Using calculus, nd Chem One's best response function and Chem Two's best response function. f) In a graph measuring Chem One's capacity along the horizontal axis and Chem Two's capacity along the vertical axis, draw the two rms' best response curves. Make sure you label the two curves correctly. g) Use the rms' best response functions to nd the Nash equilibrium capacity levels in this game. Illustrate them in your graph. h) Now, compute the market quantity and the market price when the industry is in Nash equilibrium. i) How does the government anti-trust action affect the market quantity, the market price, the consumer surplus, the industry-wide prot, and the unit cost of lysine