Problem $1($Uniform Pricing, Perfect Price discrimination$)$

A firm with market power sells its product to buyers with a demand curve Q$\_($D$)=80-2$P$.$ Suppose that the firm cannot tell what buyers have a higher reservation price than others and must sell all units of its product at the same price $($uniform$/$linear pricing$).$

$1.$ In a Price Quantity diagram, draw the firm's demand and marginal revenue curves.

To produce Q units, the firm must spend at least TC$($Q$)=0\mathrm{.}25$Q$^(2)+10$Q$+225$

$2.$ In the diagram, add the marginal cost curve and illustrate the firm's profit maximizing quantity and price.

$3.$ Using math, find the firm's profit maximizing quantity and price.

Suppose that the firm is a sole monopolist.

$4.$ When producing the profit maximizing quantity, what is the firm's profit? What is the consumer surplus?

$5.$ In this industry, what is the socially optimal quantity? What is the loss in total surplus $($deadweight loss$)$ from the

monopoly?

Suppose the firm could buy detailed information about its buyer's reservation prices. With this information, the firm could

perfectly price discriminate by selling its output on a sliding scale.

$6.$ What is the highest price the firm would be willing to pay to buy the information?