CS代写 MSIN0041 – Individual Coursework 2

MSIN0041 – Individual Coursework 2
Last update: 3 November 2022

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Problem 1. Regression-Based Demand Model

Use data() to load the tuna dataset from the bayesm package. You can view the docu-
mentation of this dataset by running ?tuna in R. From the documentation, you will see the
correspondence between each column and the different brand names.

a. (2 marks) Regress the log demand of Chicken of the Sea tuna on the log prices of all
seven brands. Show your R codes and use summary() to show the regression output.

b. (2 marks) Interpret the coefficient on LPRICE1.

c. (2 marks) Interpret the coefficient on LPRICE2.

d. (2 marks) Suppose the regression estimation is unbiased. What is the optimal cost
markup for Chicken of the Sea tuna?

Problem 2. Ad Effectiveness Measurement

Angel Hotel Group shares its customer information with Google so that whenever a user
is using Google’s search engine, the hotel would know whether the user is a registered
customer at the hotel.

Suppose the hotel’s marketing department mainly targets the hotel’s registered customers
that are searching for travel related keywords such as “hotel” on Google. For each regis-
tered customer 7, let -7 = 1 if the customer is searching for a travel-related keyword and
-7 = 0 if otherwise. For each registered customer doing a travel-related search, the hotel
is able to win the bid to push its ads to the customer with a probability of 40%. For those
registered customers not searching for travel-related keywords, they see the hotel’s ads
with a probability of 5% through internet traffic outside Google. From Google Ad’s analyt-
ics data, the proportion of registered customers’ searching for hotels on Google is about
20%. Let,7 2 {0, 1} denote a registered customer’s treatment assignment such that,7 = 1
means the customer sees the hotel’s ad whereas,7 = 0 when the customer does not see
the hotel’s ad.

Let .7 2 {0, 1} be the observed outcome where .7 = 1 if the customer 7 makes a booking
and .7 = 0 if otherwise. Each customer 7 is associated with the two potential outcomes
.7 (0) 2 {0, 1} and .7 (1) 2 {0, 1}, such that .7 = .7 (,7). We will be looking at the estimation

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of treatment effect from an omniscient view. Below is the distribution of .7 (0) and .7 (1)
conditional on -7:

Pr(.7 (0) = 1|-7 = 1) = 0.3, Pr(.7 (1) = 1|-7 = 1) = 0.4,
Pr(.7 (0) = 1|-7 = 0) = 0.01, Pr(.7 (1) = 1|-7 = 0) = 0.02.

In practice, the above distributional information is not available to the firm, but some can be
measured through data. Here is a quick summary of the data about registered customers
that can be collected by the hotel:

• Each registered customer’s observed outcome .7 2 {0, 1}.

• Each registered customer’s treatment assignment,7 2 {0, 1}.

• Each registered customer’s search pattern -7 2 {0, 1}.

Assume that for each registered customer 7, (.7 (0),.7 (1)) ?,7 |-7, ie conditional on the cus-
tomer’s search pattern, whether the customer sees the hotel’s ad is independent of the two
potential outcomes. Now the hotel is interested in knowing how effective is its advertising
to its registered customers.

a. (2 marks) Use the distributional information. Conditional on,7 = 1, what is the prob-
ability that -7 = 1? What is the probability of -7 = 1 conditional on,7 = 0? (Hint: Use
Bayes’ rule.)

b. (2 mark) Calculate the average treatment effect on the treated with the distributional
information. Why cannot the hotel directly measure ATT through the data that it can

c. (4 marks) Due the fundamental challenge to measuring ATT, the company decides to
use ⇢(.7 (1) |, = 1) � ⇢(.7 (0) |, = 0) as a proxy measure for ATT. Using the distri-
butional information, calculate the bias of this proxy measure. (Hint: Use the law of
iterated expectations.)

d. (2 marks) Explain the intuition of the bias.

e. (3 marks) Construct an unbiased estimator of ATT that is feasible given the data that
can be collected by the hotel. Remember to explain why it is unbiased.

f. (5 marks) Suppose now due to privacy regulation, the hotel is not allowed to share its
customer information with Google. Consequently, when a customer does not see the
hotel’s ad, the hotel does not know whether the customer was searching for travel-
related keywords, ie -7 is unobserved when,7 = 0. For your information, here is a
quick summary of data observable by the hotel after the privacy regulation:

• Each registered customer’s observed outcome .7 2 {0, 1}.

Passenger / carriage Economy First

Less Well-Off £1.5 £2
Well-Off £2.5 £6

Table 1: WTP of passengers

• Each registered customer’s treatment assignment,7 2 {0, 1}.

• Each registered customer’s search pattern conditional on,7 = 1.

Propose an experimental design that could help the company collect the data for an
unbiased estimator of ATT. Explain how the estimator is constructed. (Hint: In the
reading for Lecture 4, what did Rocket Fuel do to measure the advertising effectiveness for
its clients?)

Problem 3. Second-Degree Price Discrimination

Suppose you are in the 19th century and you are working for a railway company called
Monopoly Rail. The company runs a monopoly railway service connecting Liverpool and
Manchester. Currently, the company has two types of carriages for its trains: first class and
economy class. The economy class offers an okay ride between the two cities, whereas the
first class offers an extravagant one. For simplicity, assume the cost of operating each type
of carriage is 0.

Yourmarketing department has learned that the companyhas two types of passengers: the
well-off and the less well-off. The sizes of these two segments are approximately the same.
Assume the total market size is 100. Through a conjoint analysis, the company learned
about each passenger type’s willingness-to-pay for each type of carriage. The estimates
are presented in Table 1. Given a menu of options, each customer chooses the option
that gives the customer the highest surplus. If multiple options maximize the customer’s
surplus, the customer chooses among these surplus-maximizing options the one that gives
the highest WTP. Assume the firm has no supply constraint: the firm is able to service the
entire market with each type of carriage.

a. (2 marks) If the company only operates one type of carriage, which type should the
company operate and what are the optimal price and profit?

b. (4 marks) What are the optimal prices and profit if the company offers both types of
carriages?

c. (2 marks) Based on your results so far, which carriage(s) should the company offer
and at what price(s)?

d. (6 marks) The company has been thinking about new ways to improve profitability.

Passenger/

without roofs

with roofs

Less Well-Off £0.6 £1.5 £2
Well-Off £0.6 £2.5 £6

Table 2: WTP of passengers including the roofless economy

Towards this objective, the company hired a consultant to analyse its business. Af-
ter careful analysis, the consultant proposed that the company should dismantle the
roofs of its economy carriages. Understandably, the company’s executives were not
convinced of the counter-intuitive proposal at all. To show this proposal’s merits, the
consultant worked with the company’s marketing department to estimate each pas-
senger type’s WTP for each type of carriage. The results are presented in Table 2.

Riding in an economy carriage without a roof becomes very miserable when it rains.
In this case, the well-off and the less well-off suffer equally from being drenched in
rain. If the company goes ahead with dismantling the roof of the economy-class
carriages, which type(s) of carriages should the company offer and at what price(s)?
Would it be profit-improving for the company to remove the roofs?1 (Note that the
company can sell both roofed and roofless economy-class carriages)

1Assume social and legal factors such as customer backlash and regulatory response, can be ignored and
only profits are considered here.

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