Suppose consumers are willing to purchase one unit of a good. However each customer is one of two type: type H and type L. Customers types differ in their marginal benefit from quality

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July 19, 2019
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July 20, 2019
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Suppose consumers are willing to purchase one unit of a good. However each customer is one of two type: type H and type L. Customers types differ in their marginal benefit from quality

 

Question 1

a        The table below shows the monthly demand for movies for three individuals: Kat, Peeta and Primrose.

Kat
MB

($/unit)

  Sales

(units/ yr)

10.00   1
8.00   2
6.00   3
2.00   4
Peeta
MB

($/unit)

  Sales

(units/ yr)

9.00   1
4.00   2
1.00   3
0.00   4
Primrose
MB

($/unit)

  Sales

(units/ yr)

7.00   1
3.00   2
0.00   3
0.00   4

Suppose the cinema has marginal cost $3.

i           Suppose that last month the cinema only had 2 customers: Kat and Peeta. What would have been the cinema’s profit maximising linear price?

[2 marks]

ii         Suppose that this month the cinema obtained an additional customer: Primrose. (Thus this month the cinemas has 3 customers.) What would be the cinema’s new profit maximising linear price?

[2 marks]

iii        Provide intuition for the difference in your results in parts a and b.

[2 marks]

iv        In the above example, does the cinema’s profit increase or decrease when Primrose joins the market? Provide intuition for you answer.

[2 marks]

v          Would the addition of extra customers ever cause the firm’s profit to fall? Provide a succinct explanation.

[2 marks]

 

 

b          Consider the following data for three consumers.

Tyrion
MB

($ per unit)

  Sales

(units a month)

24.00   1
18.00   2
12.00   3
6.00   4
0   5
Jamie
MB

($ per unit)

  Sales

(units a month)

20.00   1
14.00   2
8.00   3
2.00   4
0   5
Cersei
MB

($/movie)

  Sales

(movies/ month)

16.00   1
7.00   2
5.00   3
0.00   4
0   5

Suppose a firm sells to these two customers, and has a fixed cost of $0 and marginal cost of $4, so that total cost is TC = 4Q, where Q represents output.

i           Find the profit maximising two part tariffs if the firm can conduct direct price discrimination, i.e can identify Tyrion and Jamie and Cersei.

[2 marks]

ii          Suppose it is possible for the firm to restrict access to those who pay an access fee. What is the profit maximising two part tariff if the firm must conduct indirect price discrimination (i.e. cannot identify Tyrion and Jamie and Cersei), but can tell whether they have paid the access fee? (In this case the firm can only distinguish between those who have a have not paid an access fee.)

[6 marks]

iii         Provide an explanation for the difference in profit you found in part a and part b?

[2 marks]

[Total: 20 marks]

 

[Word limit: 500  words]

 

Question 2

a        Suppose a coffee shop sells coffee, cake and muffins. Further assume the firm has three customers. Customers will purchase at maximum one cup of coffee and one serve of either cake or muffin (i.e. customers may have a cake or a muffin, but not both).  Each customer’s reservation price for the product given in the following table:

  Product
Coffee Cake Muffin
Customer 1 5 5 3
Customer 2 8 1 1
Customer 3 6 3 4
Customer 4 1 2 8

The firm has zero production costs.

i        Find the firm profit maximising linear prices for coffee, cake and muffin.

[2 marks]

ii       Find the profit maximising price when the firm enacts pure tying.

[2 marks]

iii      Find the profit maximising prices under mixed tying.

[3 marks]

iv      Provide intuition for the relative profitability of the three pricing strategies.

[3 marks]

If a customer is indifferent between 2 options assume the customer chooses the most expensive option.

  1. Suppose a firm has a fixed cost of $0 and marginal cost of $2, so that total cost, TC, is given by TC = 2Q, where Q represents output. Suppose it is possible to ‘bundle’ output.

Further suppose a firm sells to two customers, whose marginal benefit is given in the following tables:

Robert
Quantity

($ per unit)

  MB

($ per unit)

1   13
2   9
3   6
4   1
5   0
6   0
Ned
Quantity

($ per unit)

  MB

($ per unit)

1   7
2   4
3   3
4   2.5
5   0.5
6   0

 

i           Find the profit maximising bundles and their prices if the firm can identify  which customer is Robert and which is Ned?

[2 marks]

ii          Find the profit maximising  bundles  and prices if the firm cannot identify which customer is Robert and which is Ned?

[8  marks]

 

[Total: 20 marks]

[Word limit: 500 words]

 

Question 3

Suppose consumers are willing to purchase one unit of a good.  However each customer is one of two type: type H and type L. Customers types differ in their marginal benefit from quality. The marginal benefit of quality of each member of a given type is given in the following tables.

A type H customer
Quantity

(Production costs per unit)

  MB

($)

1   10
2   8
3   6
4   4
5   2
6   0
A type L customer
Quantity

(Production costs per unit)

  MB

($)

1   9
2   7
3   5
4   3
5   1
6   0

One firm supplies output to all customers.

a          Suppose there are 100 type H customers and 15 type L customers

i           Find the profit maximising varieties and their prices if the firm can identify which group a particular customer belongs to?

[2 marks]

ii          Find the profit maximising  varieties and prices if the firm cannot identify whether a particular customer belongs to group H or group L?

[5 marks]

b          Suppose there are 100 type H customers and 20 type L customers

i           Find the profit maximising varieties and their prices if the firm can identify which group a particular customer belongs to?

[2 marks]

ii          Find the profit maximising  varieties and prices if the firm cannot identify whether a particular customer belongs to group H or group L?

[5  marks]

c          Provide an explanation of the results you found in parts a and b.

[6  marks]

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