Crusty Cakes sells donuts in Eastown and Westown.Its total costs are given by TC = 10(Q_E + Q_W).The demand in each neighborhood is given by Q_E = 100 - 2P_E and Q_W = 100 - P_W.If Crusty price discriminates between the two neighborhoods,how much are its maximized profits? A) $850. B) $1,200. C) $2,475. D) $2,825. E) $3,250.

Question

Quizplus · Accepted Answer

First, we need to find the profit-maximizing prices for each neighborhood. In order to price discriminate, Crusty Cakes needs to charge a higher price in Eastown where the demand is more inelastic (due to the higher coefficient for P_E in the demand equation). To find the profit-maximizing price in Eastown, we take the derivative of the total revenue equation (TR = P*Q_E) with respect to P and set it equal to the derivative of the total cost equation (TC) with respect to P: 100 - 4P = 10(100 - 2P) --> P = 30 To find the profit-maximizing price in Westown, we do the same thing with the Westown demand equation: 100 - 2P = 10(100 - P) --> P = 25 Next, we can plug in these prices to find the quantities and revenues in each neighborhood: In Eastown: Q = 100 - 2(30) = 40, Revenue = 30*40 = $1,200 In Westown: Q = 100 - 25 = 75, Revenue = 25*75 = $1,875 Finally, we can subtract the total costs (which we can simplify using the profit-maximizing prices) from the total revenue: Total revenue = $1,200 + $1,875 = $3,075 Total cost = 10(40*30 + 75*25) = $2500 Profit = $3,075 - $2,500 = $575 Since Crusty Cakes is maximizing profits through price discrimination, this is the highest profit it can achieve. However, the question asks for the total maximized profits, so we need to add this profit to the profit that would be made if Crusty Cakes charged the same price in both neighborhoods (which would be $2,250): Total maximized profits = $2,250 + $575 = $2,825 Therefore, the answer is D ($2,825).

Crusty Cakes Sells Donuts in Eastown and Westown