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. The market price in this case is $____.

Question

Quizplus · Accepted Answer

In a cartel, firms maximize joint profits by acting as a monopoly. The marginal revenue (MR) is derived from the demand curve: MR = 400 - 24Q. Setting MR equal to the marginal cost (MC) of $64 gives 400 - 24Q = 64, solving for Q gives Q = 14. The total market output is 14, and each firm produces 7 units. Substituting Q = 14 into the demand curve P = 400 - 12Q gives P = 400 - 12(14) = 232.

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