Jacob Grimm sells barrels of Skull & Bones Ale to the isolated villages of Forlorn and Dismal. Because Forlorn and Dismal are separated by a high mountain range populated by werewolves and vampires, it is not possible to resell in Dismal the ale that was purchased in Forlorn, and vice versa. The respective demand equations in Forlorn and Dismal are Q

P F

= 50 − F 4 5 .

;

Q P

D

= 75 − D 7 5 .

.

Jacob’s total cost equation is TC = 10 + 0.5Q2 , where Q = QF + QD.

a. What is the profit-maximizing price and output level in each village?

b. Verify that the demand for Skull & Bones Ale is less elastic in the market in which Jacob charges the higher price.

c. Calculate Jacob’s total profit.