Question: Assume that two companies (A and B) are duopolists who produce identical products.

Demand for the products is given by the following linear demand function:

P=200 – Q_A - Q_B

where QA and Q5 are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are

\[T{{C}_{A}}=\text{ 1},\text{5}00\text{ }+\text{ 55}{{Q}_{A}}\text{ }+Q_{A}^{2}\] \[T{{C}_{B}}=\text{ 1},200\text{ }+\text{ 20}{{Q}_{B}}\text{ }+2Q_{B}^{2}\]

Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm's output will not change).

a. Determine the long-run equilibrium output and selling price for each firm.

b. Determine Firm A, Firm B, and total industry profits at the equilibrium solution found in Part (a).