Consider a natural monopoly with the following total cost function:

LRTC

$=$

$0\mathrm{.}1$

q

$3$

$$

$10$

q

$2$

$+$

$275$

q

$.$

This implies that LRMC $=0\mathrm{.}3$q$2-20$q $+275$ and LRAC $=0\mathrm{.}1$q$2-10$q $+275.$ The product demand is P $=500-10$q$.$ Given these conditions, the demand curve cuts the LRAC curve at a point where the LRAC is downward sloping.

Solve for the profit$-$maximizing unregulated monopoly price and output.

Find the unregulated monopoly$$s profits.

Now assume this monopoly is regulated. Solve for the output that the monopoly would charge if Ramsey pricing were enforced. What is the price? What is the profit to the monopolist?

Calculate the increase in consumer surplus that results from regulation.