Bathworks has exclusive rights to sell its perfumes.The demand for its perfumes faced by Bathworks is given by Q = 250 - 0.5P.Bathworks's costs are given by TC = 50Q + 5.5Q².Its maximum monopoly profit is:

Question

Quizplus · Accepted Answer

To find the maximum monopoly profit, first determine the marginal revenue (MR) and marginal cost (MC). The demand function is Q = 250 - 0.5P, so the inverse demand function is P = 500 - 2Q. Total revenue (TR) is P*Q = (500 - 2Q)Q = 500Q - 2Q^2. MR is the derivative of TR: MR = 500 - 4Q. The total cost (TC) is given as 50Q + 5.5Q^2, so MC is the derivative of TC: MC = 50 + 11Q. Set MR = MC to find Q: 500 - 4Q = 50 + 11Q, solving gives Q = 30. Substituting Q = 30 into the demand function gives P = 500 - 2(30) = 440. Profit is TR - TC = (440*30) - (50*30 + 5.5*30^2) = 13,200 - 6,450 = 6,750.

Bathworks Has Exclusive Rights to Sell Its Perfumes