Question: Suppose the microchip producer discussed in this chapter faces demand and cost equations give by Q= 8.5 - .05P and C= 100 + 38Q. Choosing to treat price as its main decision variable, the microchip producer writes profit as

\(\pi =R-C\) \(=\left[ P\left( 8.5-0.05P \right) \right]-\left[ 100+38\left( 8.5-0.05P \right) \right]\)

\(=-423+\frac{10}{4}P-0.05{{P}^{2}}\)

Derive an expression for M Π = d Π /dP. Then set M Π =0 to find the firm’s optimal price. Your result should confirm the optimal price found earlier in the chapter.