Gliberace's Fashion Accessories of Las Vegas produces gemstone-encrusted formal wear for sale in Los Angeles and San Francisco subject to total cost TC = 100 + 5(Q_LA + Q_SF).Demand for Gliberace's stones in the two cities is given by Q_LA = 70 - 2P_LA and Q_SF = 55 - P_SF.If Gliberace price discriminates between the two cities,what will its maximum profits be?

Question

Quizplus · Accepted Answer

To find the maximum profits when Gliberace price discriminates, we first determine the profit-maximizing quantity and price for each city. For Los Angeles (LA), the demand function is QS_LA = 70 - 2P_LA. For San Francisco (SF), the demand function is QS_SF = 55 - P_SF. The total cost function is TC = 100 + 5(QS_LA + QS_SF).1. For LA, to find the profit-maximizing quantity and price, we first invert the demand function to solve for P_LA in terms of QS_LA: P_LA = 35 - 0.5QS_LA. Revenue in LA (R_LA) is P_LA * QS_LA, and marginal revenue (MR_LA) is the derivative of R_LA with respect to QS_LA. Setting MR_LA equal to marginal cost (MC, the derivative of TC with respect to quantity, which is 5) and solving for QS_LA gives the profit-maximizing quantity. Then, we use the demand function to find the corresponding price.2. For SF, we follow a similar process: invert the demand function to get P_SF in terms of QS_SF, calculate R_SF and MR_SF, set MR_SF equal to MC, and solve for QS_SF. Then, use the demand function to find the corresponding price.3. Calculate total revenue (TR) by adding the revenues from both cities and subtract the total cost (TC) from TR to find total profit.After performing these calculations, we find that the profit-maximizing quantities and prices for LA and SF lead to a total profit of $975, making option D the correct answer.

Gliberace's Fashion Accessories of Las Vegas Produces Gemstone-Encrusted Formal Wear