Ralph’s firm consists of divisions A and B. All of the output of A is transferred to B, where it…

Ralph’s firm consists of divisions A and B. All of the output of A is transferred to B, where it is processed further and then sold. No costs are incurred at center. The outputs are coordinated, implying qA = qB. The market price for the finished product is presently 450 per unit; and the division’s short-run cost structures are as follows:

(a) Determine the firm’s optimal output and corresponding profit.

 (b) Suppose B can order any quantity from A, and will be charged a transfer price of T per unit. A is obliged to produce as instructed. Find a T such that maximizing its division income will lead B to prefer the output quantity you determined in (a) above.

(c) Suppose A can manufacture any quantity it desires and will be credited with an internal revenue of T for each unit. Find a T such that maximizing its division income will lead A to prefer the output quantity you determined in (b) above.

 (d) As a serious lesson in the art of coordination, we appear to be making a mistake here. What is our mistake?

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