Suppose two firms compete by choosing output levels simultaneously. If Firm 1 produces q1 units and firm 2 produces q2 units then total quantity supplied is Q=q1+q2. The market price depends on the total output, Q. The firms’ total cost functions are:

c1q1=q12 (for Firm 1)

c2q2=10q2+q22 (for Firm 2)

The market inverse demand function is: pQ=100-Q

A) Given q2, what is Firm 1’s profit maximizing level of q1? (i.e., what is Firm 1’s ‘best response’ function? This function tells Firm 1 the level of q1 that maximizes its profits for each value of q2?).

B) Given q1, what is Firm 2’s profit maximizing level of q2?

C) Solve for the equilibrium values of q1 and q2.

D) Graph the best response functions of firms 1 and 2 on the same graph and find the equilibrium point.

E) Compute the market equilibrium price and the equilibrium profit for each firm.

F) Suppose instead of acting simultaneously, that firm 1 is a leader in the industry who makes its output level publicly known before firm 2 makes its output decision. For this case, solve for the equilibrium values of q1 and q2.

G) Compute the market equilibrium price and the equilibrium profit for each firm.

H) Based on your solutions to the above parts, is it better for firm 1 to act first and announce its output level, or should it not announce its output level to firm 2? Explain.