An upstream division provides inputs (intermediate product) to a downstream division of a firm. The downstream division then manufactures and sells outputs (final product) in the market place; each unit of output requires one unit of input. The upstream division's variable (marginal) cost to produce each input is $3. In addition to any transfer price paid to upstream, the downstream division spends an additional $5 to produce each output. The firm faces a downward sloping linear demand curve in the output market: P = 15 Q / 12, where is the price and the quantity. Finally, assume that when decisions are delegated to division managers, the managers make decisions to maximize their own division's profit.

a. How many cars should the firm (which owns both upstream and downstream) optimally produce? That is, what is the production decision made by the centralized firm, and what is the resulting firm profit.

b. Calculate the firm's profit if the transfer price and the production decision are delegated to the two divisions. That is, in the delegated setting, upstream announces the per unit transfer price and downstream decides how many units to purchase.