Suppose that the market demand curve for bean sprouts is given by P = 820 - 2Q, 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 $20 per unit of output. In equilibrium, total output by the two firms will be

Question

Quizplus · Accepted Answer

Since there are two firms, the leader (Firm A) sets output first and the follower (Firm B) responds by choosing its output level.

To find the leader's output, we set the follower's best response equal to the leader's output:

Qb = (820 - P)/2 = (820 - 2QA)/2 = 410 - QA

Then we can use the leader's profit maximization condition:

MR = MC 
820 - 4QA - QB = 20 
820 - 4QA - (410 - QA) = 20 
410 = 5QA

So the leader's output is QA = 82.

The follower's output is then QB = 300 - QA = 218.

Therefore, total output by the two firms is 82 + 218 = 300.

Suppose That the Market Demand Curve for Bean Sprouts Is