Mizuno Corporation produces and sells running shoes. The marketing division (the downstream division) of Mizuno faces the following the direct market demand equation as follows:

Q = 200 - 0.5P

,where Q is the number of pairs of shoes and P is the price of a pair of shoes.

The total cost of assembling and selling shoes (excluding the leather) is

TCD = 50Q + 192.

Production of each pair of shoes requires 1 square yard of leather. The leather is shaped and cut by the Form division of Mizuno (the upstream division). The Form division's only customer is the marketing division.

The total cost function for leather is = . + + ,

where QU is the quantity of leather produced.

4.1 (7 points) Write down the profit equations of downstream division (D), upstream division (U), and total profits ().

Equations (a), (b), and (c).

D = _________________________________

U = _________________________________

= _________________________________

4.2 (7 points) Calculate the profit-maximizing quantity of shoes (Q*), quantity of leather ( ) and price of shoes (P*)

Q* = _____________ units.

QU = _____________ units.

P* = $____________.

4.3 (4 points) Determine the optimal transfer price (PU ).

PU = $______________________

4.4 (7 points) Using the profit equations of your answer in (4.1), calculate the profits earned by the downstream division (D), the upstream division (U), and total profits ().

D = $______________________________

U = $______________________________

= $______________________________