Question

3) A sticky goo oozes mysteriously from the rare wazoo tree, which grows only on the farm of Wolf Molder, just outside of Pullman, Washington. This goo, when smeared on the face, results in a tightening of the skin and the elimination of fine lines. Wolf bottles the goo at a cost of $2 per bottle and sells it to Donna Scali at a wholesale price of $w per bottle. Donna sells the goo to the general public over the Internet under the name “Youth Goo” at a price of $P per bottle. The retail demand for Youth Goo is given by P = 60 - .01Q. (a) Write Donna Scali’s profit as a function of the number of bottles of Youth Goo she sells over the Internet and the wholesale price, πD(Q;w). Write an equation characterizing Donna’s profit-maximizing choice of output as a function of the wholesale price w. (b) What is Wolf’s profit as a function of the number of bottles of Youth Goo he sells to Donna, πW(Q)? What is Wolf’s profit-maximizing choice of output? (c) What are the resulting values of the wholesale and retail prices? What are profits to Donna and Wolf? (d) Wolf offers Dana a contract in the form of two-part tariff, a wholesale price, w, and a fixed fee, F. Calculate the wholesale price that Wolf charges, the optimal quantity that Donna buys, and Donna’s optimal price. What should be the range of the fee so that Donna would accept the offer and Wolf prefers this system? (e) After a long Internet courtship, Wolf and Donna decide to become partners in business and in life. After combining their separate businesses (Youth Goo production and retail distribution, respectively), they conclude that they could make larger combined profits by choosing a different level of output. What is their new profit-maximizing level of output Q** and retail price P**? What are their new profits?

Answer 1