Suppose there is a firm with two divisions: an upstream division and a downstream division. One unit of output from the upstream or production division is used for each unit of output of the downstream division. The upstream division is the only producer of the input for the downstream division. The cost functions for the two divisions are given by:

cP

(q) = 5q cM (q) = q 2

where P and M stand for the production and marketing divisions, respectively. The inverse demand for output produced by the marketing division is given by:
p = 10

– 0.25q

(a) Determine the profit-maximizing transfer price for the firm.

(b) Calculate the output of the two divisions and the price the marketing division charges its customers if the production division sets the optimal transfer price.

(c) Suppose the firm allows the manager of the production division to set the transfer price. Determine the transfer price the manager will charge the marketing division, assuming the manager maximizes profits at the production division.

(d) Demonstrate that the firm’s profits are greater when the optimal transfer price, as opposed to the transfer price set by the manager of the production division, is set.