(From Transfer Pricing) Assume that the production division (P) of a pharmaceutical firm produces sleeping pills. It sells its product internally to its marketing division (M), which then packs and distributes its medicine to its global retail outlets. The M divisions demand (per 1000 pack) is given by: PM = 80 0.001QM, and its cost is: CM = 200,000 + 10QM. Similarly, the P divisions cost is: CP = 400,000 + 10QP + 0.001QP2. i. Assuming that there is no external market for sleeping pills, find (1) the profit maximizing output and price for the product; (2) the overall market price and output that will maximize the firms profits; (3) the optima transfer price between the P & M divisions. ii. Assume now that the drug can be sold in a competitive market at a pack price of 45 and calculate: (1) the profit-maximizing output and price for the P & D divisions and the optimal transfer price; (2) how the P division should divide its output between the open market and its own M division to maximize its profits?