An amusement park faces a demand curve of Q = 40 - 0.4P and marginal cost of MC = 1.25Q, where Q is measured in thousands of customers. The amusement park's profit-maximizing output level is ____thousand.

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Quizplus · Accepted Answer

The profit-maximizing output level is where marginal revenue equals marginal cost. Marginal revenue is the derivative of total revenue, which is equal to price times quantity. So, MR = P - 0.4P = 0.6P. Setting MR equal to MC, we get 0.6P = 1.25Q. Substituting the demand curve, we get 0.6(40 - 0.4Q) = 1.25Q. Solving for Q, we get Q = 60.

An Amusement Park Faces a Demand Curve of Q =