Problem 1: Using the Marginal Approach
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.
What are your marginal costs for each customer load level?
If you are compensated $10 per ride, what customer load would you choose? (A, B, C, or D)
Marginal Cost is the change in costs due to the additional customer. Since marginal revenue is the price of $10, you will serve customers up to the point where MR ≥ MC or you will serve 7 customers.
Marginal Cost is the change in costs due to the additional customer. Since marginal revenue is the price of $10, you will serve customers up to the point where MC < MR or you will serve 10 customers.
Marginal Cost is the change in costs due to the additional customer. Since marginal revenue is the price of $10, you will serve customers up to the point where MC< MR or you will serve 9 customers.
Marginal Cost is the change in costs due to the additional customer. Since marginal revenue is the price of $10, you will serve customers up to the point where MC = MR or you will serve 7 customers.
Problem 2: Elasticity and Pricing
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 $10 for your product. What is the price that you should charge if demand elasticity is -3?
Problem 3: Price Discrimination
An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows:
Price ($) Quantity
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. 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: (Express your answers in whole numbers for each)
The amusement park charges a different price in each market. (The adult market first chart below and fill in the red blanks, then the children’s market second chart below and fill in the red blanks)
The amusement park charges the same price in the two markets combined. (Third chart below and fill in the red blanks)
Explain the difference in the profit realized under the two situations.
Price Quantity Total Rev Marginal Rev Marginal Cost Total Cost MR-MC Profit
? 6 84 5 30 34
13 ? 91 7 5 35 2 56
12 8 96 5 5 40 0 ?
? 9 99 3 5 45 -2 54
10 ? 100 1 5 50 -4 50
9 11 99 -1 5 55 -6 ?
? 12 96 -3 5 60 -8 36
7 ? 91 -5 5 65 -10 26
6 14 84 -7 5 70 -12 ?
5 15 75 -9 5 75 -14 0
Price Quantity Total Rev Marginal Rev Marginal Cost Total Cost MR-MC Profit
14 2 28 5 10 ?
13 ? 52 12 5 20 7 32
? 6 72 10 5 30 5 42
11 8 88 8 5 40 3 48
10 10 100 6 5 50 1 ?
9 ? 108 4 5 60 -1 48
? 14 112 2 5 70 -3 42
7 16 112 0 5 80 -5 ?
6 ? 108 -2 5 90 -7 18
? 20 100 -4 5 100 -9 0
Price Quantity Total Rev Marginal Rev Marginal Cost Total Cost MR-MC Profit
14 8 112 5 40 72
? 11 143 10.33 5 55 5.33 88
12 ? 168 8.33 5 70 3.33 98
11 17 187 6.33 5 85 1.33 ?
? 20 200 4.33 5 100 -0.67 100
9 ? 207 2.33 5 115 -2.67 92
8 26 208 0.33 5 130 -4.67 ?
? 29 203 -1.67 5 145 -6.67 58
6 ? 192 -3.67 5 160 -8.67 ?
5 35 175 -7.67 5 190 -12.67 -38
Problem 4: Bundling
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.
Preferences
Showtime History Channel
Customer 1 9 2
Customer 2 3 8
Should Time Warner bundle or sell separately? (Your answer must include the unbundled and bundled profits)
Should Time Warner bundle if everyone likes Showtime more than the History channel (i.e., preferences are positively correlated).
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)? (Your answer must include the profit with mixed sharing)
