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 = 1,500 - 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, Mystic Energy earns a profit of $ ____.

Question

Quizplus · Accepted Answer

To find the profit earned by Mystic Energy, we first determine the quantity that maximizes total profit for the cartel. The total revenue (TR) is P*Q, and the total cost (TC) is the marginal cost (MC) times quantity. The profit (π) is TR - TC.Given the inverse demand curve P = 1,500 - 0.08Q and MC = $500, we first find the quantity (Q) that maximizes total profit. To do this, we set marginal revenue (MR) equal to marginal cost (MC). The marginal revenue can be found by doubling the slope of the demand curve (because of the derivative of TR with respect to Q), so MR = 1,500 - 0.16Q.Setting MR equal to MC to find the profit-maximizing quantity:1,500 - 0.16Q = 5001,000 = 0.16QQ = 6,250 (total quantity for the cartel)Since Mystic Energy and E-Storm split the market output evenly, Mystic Energy produces half of this quantity:Q_Mystic = 6,250 / 2 = 3,125 fuel cells.To find the price, we substitute Q back into the inverse demand equation:P = 1,500 - 0.08(6,250) = 1,500 - 500 = $1,000.The profit for Mystic Energy is then calculated as:π = (P - MC) * Q_Mysticπ = (1,000 - 500) * 3,125 = $500 * 3,125 = $1,531,250.

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