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. Gotcha holds to the agreement, but Ouchy decides to produce 5 more stun guns than its level under the cartel agreement. In this case, the market output is ____.

Question

Quizplus · Accepted Answer

To find the market output when Ouchy decides to produce 5 more stun guns than its level under the cartel agreement, we first need to determine the cartel output. The total quantity (Q) that maximizes total profit for the cartel can be found by setting marginal revenue (MR) equal to marginal cost (MC). The inverse demand curve is P = 400 - 12Q. To find MR, we first find the total revenue (TR) which is P*Q = (400 - 12Q)Q = 400Q - 12Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 400 - 24Q. Setting MR equal to MC (which is $64) gives us 400 - 24Q = 64, leading to 336 = 24Q, or Q = 14 for the cartel. If the output is evenly split, each firm would produce 7 units under the cartel agreement. However, Ouchy decides to produce 5 more, making its output 12 units. Gotcha produces 7 units, so the total market output when Ouchy cheats is 7 (Gotcha) + 12 (Ouchy) = 19 units.

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