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 + 10q.

Suppose the entire market for lysine is controlled by one monopolist. Suppose also that the firm cannot prevent re-sales and charges the same

price to all buyers on all units.

a) Find the monopolist's profit maximizing quantity and price.

b) Find the consumer surplus and the monopolist's accounting profit when the monopolist maximizes profit (keep in mind that accounting

profit is Revenue - TC).

c) What is the unit cost of lysine?

Now, suppose that after winning an an anti-trust law suit the government breaks the monopolist into two separate firms, Chem One and

Chem Two. Each firm would still have total cost TC = 200 + 10q. 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 firms are profit maximizers.

c) Describe Chem One's and Chem Two's strategic interaction as a game in normal form.

d) Using calculus, find Chem One's best response function and Chem Two's best response function.

e) In a graph measuring Chem One's capacity along the horizontal axis and Chem Two's capacity along the vertical axis, draw the two firms'

best response curves. Make sure you label the two curves correctly.

f) Use the firms' best response functions to find the Nash equilibrium capacity levels in this game. Illustrate them in your graph.

g) Now, compute the market quantity and the market price when the industry is in Nash equilibrium.

h) How does the government anti-trust action affect the market quantity, the market price, the consumer surplus, the industry-wide profit, and

the unit cost of lysine?