d. Solve for firm one's residual demand at the equilibrium output and calculate the firm one's price elasticity of demand in equilibrium. Use the equation that relates marginal revenue with the market price and price elasticity of demand to verify that firm one's output at the equilibrium price equals firm one's profit-maximizing output, holding firm's two output constant. (MC1 = MC2 = $20) Consider a monopolist with the following inverse demand function: P = 260 - Q. The monopolist's marginal cost of production equals $20 per unit and is constant.

Firm 1

Q = Q1 + Q2

TR1 = (260 - Q1 - Q2) Q1

MR1 = 260 - 2Q1 - Q2

Equilibrium = 240 - Q2 = 2Q1

Q1 = 120 - 0.5Q2 = Best Response

Q1 = 120 - 60 + 0.25Q1

0.75 Q1 = 60

Q1 = 80

Profit = 260 - 80 - 80 = 100

P = 100(80) - 20(80)

= $6,400

Firm 2

Q = Q1 + Q2

TR2 = (260 - Q1 - Q2) Q2

MR2 = 260 - Q1 - 2Q2

Equilibrium = 240 - Q1 = 2Q2

Q2 = 120 - 0.5Q1 = Best Response

Q2 = 120 - 0.50 (80)

= 120 - 40

Q2 = 80

Profit = 260 - 80 - 80 = 100

P = 100(80) - 20(80)

= $6,400