Suppose two firms compete in an industry with an inverse demand function given by P=200−2QP=200−2Q. Each firm has a marginal cost of $40$40.

A) Solve for the monopoly profits, quantity, and price.

B) Solve for the Cournot Nash Equilibrium. State the quantities and profits for each firm and the market price.

P = 200 - 2Q

MC = $40

A) Solve for the monopoly profits, quantity, and price.

Profit = PQ

Profit = (200 - 2Q)Q

Total Revenue = 200Q - 2Q^2

Marginal Revenue = dTR/dQ = 200 - 4Q

MR = MC

200 - 4Q = 40

Q = 40

P = 200 - 2Q

P = 200 - 2 (40)

P = $120

Monopoly Profit = (P - MC)Q

Monopoly Profit = ($120 - $40) 40

Monopoly Profit = $3200

B) Solve for the Cournot Nash Equilibrium. State the quantities and profits for each firm and the market price.

B. 1 Solving for Firm's A reaction function:

PA = 200 - 2 (qA + qB)

PA = 200 - 2qA - 2qB

Profit 1 = pAqA

TR = (200 - 2qA - 2qB) qA

TR = 200qA - 2qA^2 - 2qBqA

MR = dTR/dQ = 200 - 4qA - 2qB

MC = $40

B.2 MR = MC

200 - 4qA - 2qB = 40

Best response for firm A: qA = 40 - 0.5qB

Best response for firm B: qB = 40 - 0.5qA

B.3 Solving for qA and qB,

qA = 40 - 0.5qB

qA = 40 - 0.5 (40 - 0.5qA)

qA = 80 /3 or 26.67

qA + qB = 80/3 + 80/3

Q = 160/3 or 53.33

B.4 Solving for the market price P

P = 200 - 2Q

P = 200 - 2 (160/3)

P = $93.33

B.5 Profits

($93.33 - $40 ) 80 /3

Firm A = 1422.22

Firm B = 1422.22