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ECON3430:
MANAGERIAL ECONOMICS
Problem Set 2 (30%) Due: 16:00 Monday, June 5th, 2023
Questions
Make (and state) assumptions for all questions if a good answer requires additional information.
Explain your answers and show your reasoning.
1) Three firms, A, B and C engage in Bertrand price competition in a market with inverse demand
given by P = 123 − 2Q.
Whenever a firm undercuts the rivals’ price, it gets the entire demand. If firms charge the same
lowest price in the market, they share the market. If a firm charges a price more than any rival, it
has zero market share.
Suppose there are no fixed costs, and the marginal costs of the firms are:
c(A) = 91, c(B) = 83 and c(C) = 43.
a. Find a Nash equilibrium of this game. What are each firm’s prices and
profits? Explain your solution. (3 marks)
b. Suppose firm B leaves the market. Draw each firm’s best response on a diagram
and find a Nash equilibrium of this duopoly game.
(3 marks)
c. Suppose the above game in part b between firms A and C was the stage game of an
infinitely repeated game. Would it be possible for the two firms to collude or form a
cartel in this case? (1 mark)
2) Suppose you are a cashed-up real estate investor considering purchasing an investment property in
Brisbane to buy and then rent out.
a) Find a two-bedroom apartment that is advertised for sale (provide a web link to the example).
Given the listed (or estimated) sale price of this apartment, what would be the minimum
rental income that would make it profitable to invest in this apartment? Make and state your
assumptions (e.g., interest/discount rates, maintenance costs). (3 marks)
b) Suppose interest rates went up. Would you now be willing to pay more or less for the same
property? (1 mark)
3) Price discrimination
a) Give a real-world example of group (third-degree) price discrimination (provide a web link to
the example). (1 mark)
b) Discuss what prevents re-sale in your example (i.e., why can’t people who pay the lower price
resell the good to people who face a higher price?). (2 marks)
c) In your example, is the lower price labelled as a discount or the higher price labelled as a
surcharge? Discuss how the different framing might affect revenues. (1 mark)
2
4) Information goods and the left-digit bias
a) Give a real-world example of an information good priced in a way to take advantage of the
left-digit bias (provide a web link to the example). (1 mark)
b) Information goods have properties that can lead to market failures. What are two solutions
that exist in this market that addresses market failures associated with information goods? (2
marks)
c) Briefly describe the left-digit bias and draw how the demand curve is likely to look like if the
consumers of the good in your example are left-digit biased. (2 marks)
d) Suppose the seller of this good is interested in understanding the causal effect of left-digit
bias pricing on revenues. Describe how the seller might be able to use any two of the four
empirical methods (randomised experiment, instrumental variable, difference-in-differences,
regression discontinuity) presented in the lectures for this purpose. For each method,
describe the data you would need and discuss the potential limitations/challenges of
applying that method. (4 marks)
5) Suppose you are the CEO of a brand-new social networking app (Flutter) that is exclusive to
international students in Australia. The number of users (i.e., total quantity demanded) for Flutter
is:
= 18000 − + ℎ ∈ (0,1), ℎ , ℎ .
a) Interpret the parameter . What strategies can a company like Flutter use to increase the
value of ? (2 marks)
b) Assume = 0.4 ℎ ℎ = , and the marginal cost
per user is 0. What is the profit-maximising price? (2 marks)
c) Suppose Flutter have an investment opportunity to acquire a new technology that can
increase the parameter 0.4 0.7. What is the maximum amount Flutter should be
willing to pay for this acquisition? (2 marks)