Question

1)

Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 300 – 4(Q₁ + Q₂), where P is the market price, Q₁ is the quantity demanded by Firm 1, and Q₂ is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $65.

The cournot-duopoly equilibrium quantity produced by each firm is _____.

Hint: Write your answer to two decimal places.

2)

Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 300 – 4(Q₁ + Q₂), where P is the market price, Q₁ is the quantity demanded by Firm 1, and Q₂ is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $71.

The cournot-duopoly equilibrium profit for each firm is _____.

Answer 1

(1)

Market demand: P = 300 - 4Q1 - 4Q2

Marginal cost: MC1 = MC2 = 65

For firm 1,

Total revenue (TR1) = P x Q1 = 300Q1 - 4Q1² - 4Q1Q2

Marginal revenue (MR1) = TR1/Q1 = 300 - 8Q1 - 4Q2

Setting MR1 equal to MC1,

300 - 8Q1 - 4Q2 = 65

8Q1 + 4Q2 = 235...........(1) [Reaction function, Firm 1]

For firm 2,

Total revenue (TR2) = P x Q2 = 300Q2 - 4Q1Q2 - 4Q2²

Marginal revenue (MR2) = TR2/Q2 = 300 - 4Q1 - 8Q2

Setting MR2 equal to MC2,

300 - 4Q1 - 8Q2 = 65

4Q1 + 8Q2 = 235...........(2) [Reaction function, Firm 2]

Cournot equilibrium requires solving equations (1) and (2). Multiplying equation (2) by 2,

8Q1 + 16Q2 = 470.........(3)

8Q1 + 4Q2 = 235.........(1)

(3) - (1) results:

12Q2 = 235

Q2 = 19.58

Q1 = (235 - 8Q2)/4 [Using equation (2)] = [235 - (8 x 19.58)]/4 = (235 - 156.64)/4 = 78.36/4 = 19.58

NOTE: As per Answering Policy, 1st question is answered.