A monopoly faces the demand function Q = 30 – p. Its inverse demand function is therefore p = 30 -..

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
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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. (Hint: See Q&A 9.3.)

 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.)

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