Suppose duopolists face the market inverse demand curve P = 100 - Q,Q = q₁ + q₂,and both firms have a constant marginal cost of 10 and no fixed costs.If firm 1 is a Stackelberg leader and firm 2's best response function is ,at the Nash-Stackelberg equilibrium firm 2's profit is

Question

Quizplus · Accepted Answer

To find the Nash-Stackelberg equilibrium, we first need to solve for firm 1's output level as the leader.

Taking the derivative of the inverse demand function, we get:

P = 100 - Q

MR = 100 - 2Q

Setting MR equal to firm 1's constant marginal cost of 10, we get:

10 = 100 - 2Q1

Q1 = 45

Now, we can solve for firm 2's output level using its best response function:

Q2 = 22.5 - 0.5(Q1)

Q2 = 22.5 - 0.5(45)

Q2 = 0

Since firm 2's output level is 0, its profit at the Nash-Stackelberg equilibrium is:

π2 = (100 - 0 - 10) x 0 = 0

Therefore, the correct answer is C) 800, since the question is asking for firm 2's profit, not total industry profit.

Suppose Duopolists Face the Market Inverse Demand Curve P =