Suppose there are two separate firms. The upstream firm is the only producer of an input required by the downstream firm and the upstream firm has no other customers. One unit of input at the downstream firm is required to produce one unit of output at the downstream firm. The cost functions for the two firms are:

cU (q) = 4q 2

– 2q cD (q) = q 2

+ 10q where U and D stand for the upstream and downstream firms, respectively.

The inverse demand for output produced by the downstream firm is given by:

p = 100

– q

(a) Determine the demand for output at the upstream firm from the downstream firm as a function of the price charged by the upstream firm.

(b) Determine the price the upstream firm will charge the downstream firm for the output produced by the upstream firm.

(c) Suppose the two firms were to merge and maximize joint profits.

Determine the price the upstream division will charge the downstream division, that is determine the optimal transfer price.

(d) Show that profits are greater at the merged firm than at when the two firms were operating as separate entities. What problems is the merger likely to face?