Marginal costs for each customer load level

Week 5, Problem Set Questions:

 

Question 1

Suppose your company runs a shuttle business of 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?

Q TC MC Total Rev Profit
1 30   10 -20
2 32 2 20 -12
3 35 3 30 -5
4 38 3 40 2
5 42 4 50 8
6 48 6 60 12
7 57 9 70  

 

Question 2

Suppose your company runs a shuttle business of 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.

If you are compensated $10 per ride, what customer load would you choose?

 

    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.

 

 

Question 3

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. If demand elasticity is -3, you should charge [x].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 4

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

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.

 

 

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

 

 

 Calculate the price, quantity, and profit if: The amusement park charges a different price in the adult market

Please express your answers for Price and Profit in whole dollars (i.e.10.00)

Please use whole numbers for Quanitity (i.e. 10, 27, 4)

 

Price Quantity Total

Revenue

Marginal

Revenue

Marginal

Cost

Total

  Cost

MR-MC Profit
14 6 84   5 30   34
13 7 91 7 5 35 2 56
12 8 96 5 5 40 0  
11 9 99 3 5 45 -2 54
10 10 100 1 5 50 -4 50
9 11 99 -1 5 55 -6  
8 12 96 -3 5 60 -8 36
7 13 91 -5 5 65 -10 26
6 14 84 -7 5 70 -12  
5 15 75 -9 5 75 -14 0

 

Question 5

 

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

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.

 

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

 

 

 Calculate the price, quantity, and profit if: The amusement park charges a different price in the child’s market

Please express your answers for Price and Profit in whole dollars (i.e.10.00)

Please use whole numbers for Quanitity (i.e. 10, 27, 4)

 

Price Quantity Total

Revenue

Marginal

Revenue

Marginal

Cost

Total

Cost

MR-MC Profit
14 2 28   5 10   18
13 4 52 12 5 20 7 32
12 6 72 10 5 30 5 42
11 8 88 8 5 40 3 48
10 10 100 6 5 50 1 50
9 12 108 4 5 60 -1 48
8 14 112 2 5 70 -3 42
7 16 112 0 5 80 -5 32
6 18 108 -2 5 90 -7 18
5 20 100 -4 5 100 -9 0

 

Question 6

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

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.

 

 

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

 

 

 Calculate the price, quantity, and profit if: The amusement park charges the same price in the two markets combined

Please express your answers for Price and Profit in whole dollars (i.e.10.00)

Please use whole numbers for Quanitity (i.e. 10, 27, 4)

 

  Price Quantity Total

Revenue

Marginal

Revenue

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

 

 

Question 7

Explain the difference in the profit realized under the two situations (the price in each market or in the two markets combined.)

 

Make sure you include the profit with and without price discrimination in your answer.

 

 

 

 

 

 

 

 

 

 

Question 8

 

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 Chanel
Customer 1 9 2
Customer 2 3 8

 

 

Should Time Warner bundle or sell separately?  Your answer needs to include the unbundled and bundled profits. 

 

 

Question 9

 

Suppose Time Warner could sell Showtime for $9, and History channel for $8, while making 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 bundling.


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