Chapter 2.7, Problem 17E

Price Setting The monthly demand equation for an electric utility company is estimated to be

$p=60-\left({10}^{-5}\right)x$, where $p$ is measured in dollars and $x$ is measured in thousands of kilowatt-hours. The utility has fixed costs of $7$ million dollars per month and variable cost of $\$30$ per $1000$ kilowatt-hours of electricity generated, so the cost function is

$C\left(x\right)={7.10}^6+30x$.

a. Find the value of $x$ and the corresponding price for $1000$ kilowatt-hours that maximize the utility’s profit.

b. Suppose that rising fuel costs increase the utility’s variable costs form $\$30$ to $\$40$, so its new cost function is

$C\left(x\right)={7.16}^6+40x$.

Should the utility pass all this increase of $\$10$ per thousand kilowatt-hours on to consumers? Explain your answer.