Suppose that the market demand curve for bean sprouts is given by P = 880 - 4Q, where P is the price and Q is the total industry output. Suppose that the industry has two firms, a Stackelberg leader and a follower. Each firm has a constant marginal cost of $80 per unit of output. In equilibrium, total output by the two firms will be

Question

Quizplus · Accepted Answer

In Stackelberg duopoly, the leader firm first chooses its output level, and then the follower firm chooses its output level accordingly. To find the leader's output, we set the follower's best response to the leader's output equal to the leader's output.

The follower's best response is to maximize profit given the leader's output, which is: 
Q_f = (880 - P)/8 = (880 - 4Q_l)/8 = 110 - 0.5Q_l

Setting Q_f = Q_l, we get: 
Q_l = 110 - 0.5Q_l 
1.5Q_l = 110 
Q_l = 73.33

So, the leader firm's output is 73.33 units, and the follower's output is: 
Q_f = 110 - 0.5Q_l = 110 - 0.5(73.33) = 150

Therefore, the total industry output is 73.33 + 150 = 223.33 or approximately 150 units, which is answer choice C.

Suppose That the Market Demand Curve for Bean Sprouts Is