An amusement park, whose customer set is made up of two markets

An amusement park, whose customer set is made up of two markets, adults and children,

has developed demand schedules as follows:

Quantity

Price ($) Adults Children

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: Because marginal cost is a

constant, so is average variable cost. Ignore fixed cost.) The owners of the amusement park

want 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 subscript 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 = 30 - 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.

11. George’s Pants Store sells a particular brand of slacks. It recently decreased the price of a

popular brand by 5 percent. This decrease was followed by a 20 percent increase in sales.

The marginal cost of producing these slacks is $100.

a. What is the point price elasticity of demand for these slacks?

b. What would be the optimal markup and price of these items?