Simpson Flanders, Inc., is a Motor City-based manufacturer and distributor of valves used in nuclear power plants. Currently, all output is sold to North American customers. Demand and marginal revenue curves for the firm are as follows:

P = $1,000 ‑ $0.015Q

MR = ∂TR/∂Q = $1,000 ‑ $0.03Q

Relevant total cost, marginal cost, and profit functions are

TC = $1,500,000 + $600Q + $0.005Q2

MC = ∂TC/∂Q = $600 + $0.01Q

π = TR - TC

= -$0.02Q2 + $400Q - $1,500,000

A. Calculate the profit-maximizing activity level for Simpson Flanders when the firm is operated as an integrated unit.

B. Assume that the company is reorganized into two independent profit centers with the following cost conditions:

TC Mfg = $1,250,000 + $500Q + $0.005Q2

MC Mfg = ∂TC Mfg/∂Q =500 + $0.01Q

TC Distr = $250,000 + $100Q

MC Distr = ∂TC Distr/∂Q =$100.

Calculate the transfer price that ensures a profit-maximizing level of profit for the firm, with divisional operation based on the assumption that all output produced is to be transferred internally.

C. Now assume that a major distributor in the European market offers to buy as many valves as Simpson Flanders wishes to offer at a price of $645. No impact on demand from the company’s North American customers is expected, and current facilities can be used to supply both markets. Calculate the company’s optimal price(s), output(s), and profits in this situation.