Question $18(2$ points$)$ Retake question

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

$P=1000-0\mathrm{.}015Q$

$MR=1000-0\mathrm{.}03Q$

Relevant total cost, marginal cost, and profit functions are:

$TC=1,500,000+600Q+0\mathrm{.}005Q^2$

$MC=600+0\mathrm{.}01Q$

Profit $=-1,500,000+400Q-4\mathrm{.}02Q^2$

Suppose that the firm was reorganized into two independent profit centers $(M=$ manufacturing and $D=$ distribution$)$ with the following cost conditions:

$T{C}_M=1,250,000+500Q+0\mathrm{.}005Q^2$

$M{C}_M=500+0\mathrm{.}01Q$

$T{C}_D=250,000+100Q$

$M{C}_D=100$

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 from the company's North American customers is expected and current facilities can be used to supply both markets.