8.2 A monopoly faces the demand function Q = 30 - p.

Its inverse demand function is therefore p = 30 - Q, so its marginal revenue function is MR = 30 - 2Q.

The firm’s cost function is C = 6Q + Q2, so its marginal cost is MC = 6 + 2Q. The monopoly sets its price. Its quantity is determined by the demand function.

a. Create a spreadsheet with headings Price, Quantity, Revenue, Cost, Profit, Marginal Revenue, and Marginal Cost. Enter prices ranging from 15 to 30 in increments of one in Column A

(the price column). Enter the appropriate formulas in the other cells in the spreadsheet to calculate the values of the other variables for each price. For example, the price of 15 goes in cell A2, the quantity demanded at that price goes in cell B2, the resulting revenue at that price and quantity goes in cell C2, and so on.

Find the price that maximizes profit and verify that MR = MC at this price.

b. Add columns for consumer surplus and total surplus in your spreadsheet. The formula for consumer surplus is CS = 0.5(30 - p)Q.

The firm’s producer surplus equals its profit because it has no fixed cost. Total surplus is the sum of the consumer surplus and the producer surplus. Find the price that maximizes total surplus and verify that p = MC at this price. If the profit-maximizing monopoly price is charged instead of the price that maximizes total surplus, what is the deadweight loss?

c. In addition to using the method described in parts a and

b, use Excel’s Solver tool to find the price that maximizes profit and the price that maximizes consumer surplus. (Hint: See the instructions for using Solver in Question 6.2 of Chapter 8 or use Excel’s Help feature.)