Question

Two firms compete as a Stackelberg duopoly. Firm 1 is the market leader. The inverse market demand they face is P = 62 - 2Q, where Q=Q1+Q2. The cost function for each firm is C(Q) = 6Q. Given that firm 2's reaction function is given by Q2 = 14 - 0.5Q1, the optimal outputs of the two firms are:

a. Q_L = 9.33; Q_F = 9.33.

b. Q_L = 14; Q_F = 7.

c. Q_L = 6; Q_F = 3.

d. None of the statements associated with this question are correct.

Answer 1

Ans. Option b

Substituting firm 2's response function in the inverse market demand function, we get

P = 62 - 2*(Q1 + 14 - 0.5Q1)

=> P = 34 - Q1

The firm 1's total revenue, TR1 = P*Q1 = 34Q1 - Q1^2

=> Marginal Revenue of firm 1, MR1 = dTR1/dQ1 = 34 - 2Q1

Ans Cost function for firm 1, C = 6Q1

=> Marginal cost of firm 1, MC1 = dC/dQ1 = 6

At profit maximizing level of output,

MR1 = MC1

=> 34 - 2Q1 = 6

=> Q1 = 14 units

Substituting Q1 = 14 units in the response funtion of firm 2, we get,

Q2 = 7 units

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