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 Q₀ = 500P^-^3/2 while demand by those under 65 years old is Q_y = 50P^-⁴.If the marginal cost of a ticket is $4, how should tickets to Mr.Floren's concerts be priced to maximize profits? A)$16 for senior citizens and $6 for those younger B)$12 for senior citizens and $5.33 for those younger C)$6.29 for all tickets D)$4 for senior citizens and $10.67 for those younger E)$8 for senior citizens and $16 for those younger

Question

Quizplus · Accepted Answer

To maximize profits, the price should be set where marginal revenue equals marginal cost. First, we need to solve for the demand equation for each market segment. For senior citizens: Q₀ F1F1F1S1F1F1F10 500PF1F1F1S1^F1F1F10^3/2 500 - 13/2 P = 0 P = $76.92 For those under 65 years old: Q_y F1F1F1S1F1F1F10 50PF1F1F1S1^F1F1F10⁴ 50 - 14 P = 0 P = $3.57 Therefore, the optimal ticket prices are $12 for senior citizens and $5.33 for those under 65 years old.

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