Consider a market consisting of two firms where the inverse demand curve is given by P = 500 - 2(Q₁ + Q₂).If the Stackelberg leader's and follower's marginal costs are zero, the leader's marginal revenue is A)MR(Q_L, Q_F) = 125 - Q_L + 0.5Q_F. B) MR(Q_L) = 250 - 2Q_L. C)MR(Q_F) = 250 - 2Q_F. D)MR(Q_L, Q_F) = 125 - 0.5Q_L + Q_F.

Question

Quizplus · Accepted Answer

For the Stackelberg leader, the first step is to determine the follower's best response function. The follower's profit maximization problem is:

max QS1U1B1F 500 - 2(QS1U1B11S1U1B0 + QS1U1B12S1U1B0 - QS1U1B1F) QS1U1B1F

Solving for the best response function yields:

QS1U1B1F = 250 - 0.5QS1U1B11S1U1B0 - 0.5QS1U1B12S1U1B0

Plugging this into the inverse demand equation yields:

P = 500 - 2(QS1U1B11S1U1B0 + QS1U1B12S1U1B0 - QS1U1B1F)
P = 500 - 2(QS1U1B11S1U1B0 + QS1U1B12S1U1B0 - (250 - 0.5QS1U1B11S1U1B0 - 0.5QS1U1B12S1U1B0))
P = 250 - QS1U1B11S1U1B0 - QS1U1B12S1U1B0 + 0.5QS1U1B1LS1U1B0 + 0.5QS1U1B1FS1U1B0

Taking the derivative of P with respect to QS1U1B1LS1U1B0 yields the leader's marginal revenue:

MR(QS1U1B1LS1U1B0) = 250 - 2QS1U1B1LS1U1B0

Therefore, the answer is B.

Consider a Market Consisting of Two Firms Where the Inverse