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Problem Set

Due Week 5 and worth 250 points

Problem 1: Using the Marginal Approach (40 points)

Suppose your company runs the shuttle business for a hotel to and from the local airport. The costs for different customer loads are:

1 customer:  $30

2 customers: $32

3 customers: $35

4 customers: $38

5 customers: $42

6 customers: $48

7 customers: $57

8 customers: $68.

  1. What are your marginal costs for each customer load level?
  2. If you are compensated $10 per ride, what customer load would you choose?

Problem 2: Elasticity and Pricing (40 points)

Suppose the number of firms you compete with has recently increased. You estimated that as a result of the increased competition, the demand elasticity has increased from 2 to 3 (i.e., you face more elastic demand). You are currently charging $10 for your product. What is the price that you should charge if demand elasticity is -3?

Problem 3: Price Discrimination (40 points)

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

Price ($)      Quantity of Adults           Quantity of 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. Because marginal cost is a constant, so is average variable cost. Ignore fixed costs. The owners of the amusement part want to maximize profits.

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.

Problem 4: Bundling (40 points)

Time Warner could offer the History channel (H) and Showtime (S) individually or as a bundle of both.

Suppose the reservation prices of customers 1 and 2 (the highest prices they are willing to pay) are presented in the boxes below.

The cost to Time Warner is $1 per customer for licensing fees.


                                           Showtime              History Channel

Customer 1                              9                                  2

Customer 2                              3                                  8

  1. Should Time Warner bundle or sell separately?
  2. Should Time Warner bundle if everyone likes Showtime more than the History channel (i.e., preferences are positively correlated).
  3. Suppose Time Warner could sell Showtime for $9, and History channel for $8, while making a Showtime-History bundle available for $13. Should it use mixed bundling (i.e., sells products both separately and as a bundle)?
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