The inverse demand for sandwiches over the lunch hour is given by P = 8 - 0.01Q, where P is the price per sandwich and Q is the total number of sandwiches brought to market. There are two sandwich shops operating in the local market. Firm 1's cost function is C1 = 0.000 2q12 , where q1 is the number of sandwiches brought to market by Firm 1. Firm 2's cost function is C2 = 0.000 2q22, where q2 is the number of sandwiches brought to market by Firm 2. Given that the two firms compete by setting output (Cournot), answer the following:
a. Write Firm 1's profit function. Note that Q = q1 + q2.
b. Identify Firm 1's reaction function to Firm 2's output.
c. Identify Firm 2's reaction function to Firm 1's output.
d. Identify the equilibrium output level of each firm and the equilibrium price for sandwiches.