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# maximum profit

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An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows:

Quantity
5 15 20
6 14 18
7 13 16
8 12 14
9 11 12
10 10 10
11 9 8
12 8 6
13 7 4
14 6 2

The marginal operating cost of each unit of quantity is \$5. (Hint: Since marginal cost is a constant, so is average variable cost. Ignore fixed cost.) The owners of the amusement park wish to maximize profits.

a. Calculate the price, quantity, and profit if
(1) The amusement park charges a different price in each market.
(2) The amusement park charges the same price in the two markets combined.
(3) Explain the difference in the profit realized under the two situations.
b. (Mathematical solution) The demand schedules presented in problem 2 can be expressed in equation form as follows where subscription A refers to the adult market, subscript C to the market for children, and subscript T to the two markets combined):

QA = 20 - 1PA
QC = 20 - 2PC
QT = 50 - 3PT

Solve these equations for the maximum profit that the amusement park will attain when it charges different prices in the two markets and when it charges a single price for the combined market.

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Book Title: Managerial Economics
Author: Economic Tools for Today's Decision Makers, Fourth Edition by Paul G.Keat and Philip K. Y. Youn

https://brainmass.com/economics/principles-of-mathematical-economics/maximum-profit-72054

#### Solution Summary

Determine maximum profit.

\$2.19

## Managerial Economics: Calculating Maximum Profit and Revenue

A monopolist's demand function is given by
P = 80-3Q
(with MR = 80-6Q).

Its total cost function is
TC = 20Q + 200
(with MC = 20).

(i) Using algebra determine the profit maximizing output, price and optimal profit for the firm.

(ii) Suppose that instead of maximizing profit, the firm wants to maximize total revenue. Using algebra determine the optimal output, price, profit and revenue for the firm.

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