Gotcha, the only seller of stun guns, faces the inverse market demand curve P = 400 - 12Q, where Q measures the number of stun guns per day and P is the price per stun gun. The marginal cost is constant at $64. Suppose a new firm, Ouchy, enters the stun gun market. Ouchy's marginal cost is also constant at $64. Gotcha and Ouchy agree to form a cartel and evenly split the market output. In this case, Ouchy's output level is ____.

Question

Quizplus · Accepted Answer

To find Ouchy's output level, first, determine the total output for the cartel by equating marginal cost (MC) to marginal revenue (MR). The inverse demand curve is P = 400 - 12Q. To find MR, differentiate total revenue (TR = P*Q = (400 - 12Q)Q) with respect to Q, which gives MR = 400 - 24Q. Setting MR equal to MC (64) and solving for Q gives the total quantity produced by the cartel. 400 - 24Q = 64, so 336 = 24Q, and Q = 14. Since the output is evenly split, Ouchy's output level is 14/2 = 7.

Gotcha, the Only Seller of Stun Guns, Faces the Inverse