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, Gotcha's output level is ____.

Question

Quizplus · Accepted Answer

To find Gotcha's output level when forming a cartel with Ouchy and splitting the market evenly, first, we need to determine the total quantity supplied by the cartel that maximizes total profit. The inverse market demand curve is P = 400 - 12Q. Since the marginal cost (MC) is constant at $64 for both firms, we set the marginal revenue (MR) equal to the marginal cost to find the profit-maximizing quantity for the cartel.First, find the total revenue (TR) equation by integrating the inverse demand function: TR = P*Q = (400 - 12Q)Q. To find MR, differentiate TR with respect to Q: MR = d(TR)/dQ = 400 - 24Q.Set MR equal to MC to find the profit-maximizing quantity for the cartel: 400 - 24Q = 64. Solving for Q gives Q = (400 - 64) / 24 = 336 / 24 = 14.Since Gotcha and Ouchy agree to split the market output evenly, Gotcha's output level is Q/2 = 14/2 = 7.

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