Suppose the microchip producer discussed in this chapter faces demand and cost equations given by Q = 8.5 - .05P and C = 100 + 38Q. Choosing to treat price as its main decision variable, it writes profit as
π = R - C
= [P(8.5 - .05P)] - [100 + (38)(8.5 -.05P)]
= - 423 + 10.4P - .05P2.
Derive an expression for Mπ = dπ/dP. Then set Mπ =0 to find the firm’s optimal price. Your result should confirm the optimal price found earlier in the chapter.