Miron Floren, of Lawrence Welk Show fame, now tours the country performing at accordion concerts. A careful analysis of demand for tickets to Mr. Floren's concerts reveals a strange segmentation in the market. Demand for tickets by senior citizens is described by while demand by those under 65 years old is Q_y = 50P^-⁵. If the marginal cost of a ticket is $3, how should tickets to Mr. Floren's concerts be priced to maximize profits?

Question

Quizplus · Accepted Answer

To maximize profits, we need to set the price where marginal revenue equals marginal cost. For senior citizens: Marginal revenue = 11ea6c55_6e4a_14de_9875_af94e1ce51ac_TB6162_11' = $9 Marginal cost = $3 Setting marginal revenue equal to marginal cost: 9 = 3 + 3t t = 2 So the optimal price for senior citizens is $9 per ticket. For those under 65: Marginal revenue = Q_y/P^-⁵' = $5 Marginal cost = $3 Setting marginal revenue equal to marginal cost: 5 = 3 + 3t t = 2/3 So the optimal price for those under 65 is $3.75 per ticket. Therefore, the best choice is (C), with prices of $9 for senior citizens and $3.75 for those under 65.

Miron Floren, of Lawrence Welk Show Fame, Now Tours the Country