b. Find the optimal price by hand. (Hint:Vary price while comparing

cells E12 and F12. When (P MC)/P exactly equals 1/EP, the

markup rule is satisfied and the optimal price has been identified.)

c. Use your spreadsheet’s optimizer to confirm the optimal price.

116 Chapter 3 Demand Analysis and Optimal Pricing

ABCDEFG

1

2 THE OPTIMAL PRICE FOR SPARE PARTS

3

4

5 Price Quantity Revenue Cost Profit

6

7 780 10 7,800 22,050 14,250

8

9

10 Elasticity MC (PMC)/P 1/EP

11

12 39.0 210 0.7308 0.0256

13

S2. On a popular air route, an airline offers two classes of service: business

class (B) and economy class (E). The respective demands are given by:

Because of ticketing restrictions, business travelers cannot take

advantage of economy’s low fares. The airline operates two flights

daily. Each flight has a capacity of 200 passengers. The cost per flight

is $20,000.

a. The airline seeks to maximize the total revenue it obtains from the

two flights. To address this question, create a spreadsheet patterned

on the example shown. (In your spreadsheet, only cells E2, E3, E4,

C9, and D9 should contain numerical values. The numbers in all

other cells are computed by using spreadsheet formulas. For instance,

the total available seats in cell E5 is defined as the product of cells E2

and E3.)

b. What fares should the airline charge, and how many passengers will

buy tickets of each type? Remember that maximum revenue is

obtained by setting MRBequal to MRE. After you have explored the

decision by hand, confirm your answer using your spreadsheet’s

optimizer. (Hint:Be sure to include the constraint that the total

PB 540 .5QB and PE 380 .25QE.

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