Suppose that Mystic Energy and E-Storm are the only two producers of hydrogen fuel cells. The market inverse demand curve for hydrogen fuel cells is P = 1,300 - 0.08Q, where Q is the number of fuels cells per month and P is the price per fuel cell. The marginal cost is constant at $500. Acting as a cartel, the owners of Mystic Energy and E-Storm agree to evenly split the market output. In this case, E-Storm produces ____.

Question

Quizplus · Accepted Answer

To find the quantity produced by E-Storm when acting as a cartel, we first determine the total quantity produced by the cartel to maximize profit. The marginal revenue (MR) equals the marginal cost (MC) at the profit-maximizing output. The inverse demand curve is P = 1,300 - 0.08Q. To find MR, we first find the total revenue (TR) which is P*Q = (1,300 - 0.08Q)Q = 1,300Q - 0.08Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 1,300 - 0.16Q. Setting MR equal to MC ($500) to find the profit-maximizing quantity: 1,300 - 0.16Q = 500, which simplifies to 800 = 0.16Q, or Q = 5,000 for the total market. Since the market output is evenly split, E-Storm produces half of 5,000, which is 2,500 fuel cells.

Suppose That Mystic Energy and E-Storm Are the Only Two