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ECON20005: COMPETITION AND STRATEGY
Assignment
Administrative Rules
Due date: 4pm on Friday, 20 October
Submit your solution as one pdf file via Gradescope following the instructions provided
on the website.
The assignment is worth up to 10% of your final mark. You need to show all your work
to get partial or full credit.
The assignment may be submitted late up to 2 days after the deadline with a 15%
penalty per day.
Students are allowed to work together, but each must submit their own unique final
copy of the assignment.
Throughout: “NE” refers to Nash Equilibrium/Equilibria; “SPNE” refers to Subgame
Perfect Nash Equilibrium/Equilibria; “PSNE ” refers to Pure-strategy Nash Equilib-
rium/Equilibria.
Throughout: ”Briefly explain” means explain in no more than 3 sentences.
ECON20005 Assignment 2 1
Question 1 (15 marks) A used car company, Best Choice, is looking to sell used cars to
students. After a few months in business, it has become known among the students that 40%
of the cars sold by the company are ”junk,” while the remaining 60% work fine and are ”not-
junk.” Unfortunately for the students, there is asymmetric information: The salespeople at
Best Choice know whether a given car is junk while students do not.
Suppose it is commonly known that Best Choice values junk and not-junk cars by V sjunk =
1000 and V snot−junk = 6000, and that students value junk and not-junk cars by V
b
junk = 2500
and V bnot−junk = 7500. Assume there are sufficiently many students wanting cars such that
the market price for a given car, P , is bid up to students’ expected value for that car.
Further, assume that a student gets a payoff of 0 if they do not purchase a car at all, and
that Best Choice sells a car if it is indifferent between keeping the car and selling it.
(a) (5 marks) Would both the junk and not-junk cars be exchanged if both Best Choice and
the students had complete information over whether a given car was junk or not? For
what range of junk and not-junk prices could these cars be exchanged under complete
information? Explain briefly.
(b) (5 marks) What is the market price for cars under asymmetric information? Do both
types of cars get exchanged under asymmetric information? Explain briefly.
(c) (5 marks) What is the maximum percentage of junk cars that Best Choice can offer
such that both types of cars get exchanged under asymmetric information? What is
the market price for cars at this maximum percentage?
Question 2 (25 marks) Consider a Linear City Model with three firms, A, B and C. Firm
A is at location 0, firm B is at location 1/2 and firm C is at location 1. Firms’ marginal
costs are c = 1 and consumers’ cost of traveling a distance of 1 is t = 3. There are 100
consumers uniformly located over the Linear City. The firms’ prices are denoted by pA, pB
and pC . Assume that every consumer is buying.
(a) (10 marks) Derive the demand functions of the three firms.
(b) (10 marks) Suppose firms A, B and C compete by setting prices simultaneously. Find
the NE prices and profits of this game. Do all firms charge the same price and earn
the same profit? Briefly explain.
(c) (5 marks) Now assume prices are fixed at p = 20 for all firms. Firms A, B and C
compete by making location choices simultaneously. Is having firm A at location 0,
firm B at location 1/2, and firm C at location 1 a pure-strategy Nash Equilibrium?
Briefly explain.
ECON20005 Assignment 2 2
Question 3 (25 marks) The Green Delight is a reputable vegan burger joint in Melbourne.
The owner of the Green Delight aims to sell as many burgers as possible, but this will depend
on how tasty the burgers are. If the burgers are tasty, she will sell 150 burgers. If they are
not tasty, only 50 burgers will be sold. The price of each burger is $10. The probability
of the burgers being tasty depends on the effort of the cook. The likelihood of producing
tasty burgers is 80% if the cook puts in high effort and 30% if the cook puts in low effort.
Providing effort is costly. The cook gets a disutility of $700 from putting in high effort, and
a disutility of only $100 from putting in low effort. If the cook does not work at the Green
Delight, there is another restaurant nearby providing him with an outside option of $200.
(a) (5 marks) Suppose that the owner cannot observe how much effort the cook exerts.
Assume that the owner offers a contract consisting of a base salary (w) and a bonus
(b) if the burgers are tasty. Write down the conditions which need to be satisfied for
high effort provision. Draw the constraints and show the set of contracts which satisfy
the conditions for high effort provision.
(b) (4 marks) Assuming that the base salary cannot be negative, find a contract that gives
incentives for high effort provision. Label it on the graph you drew in part (a).
(c) (5 marks) Will the owner offer the contract you found in part (b), or will she be better
off with a contract where low effort is provided? Explain.
(d) (5 marks) Now, suppose that the owner can send the cook to a cooking school which
will reduce the cook’s cost of high effort by half. Assume that the cooking school’s fee
is $100. After the cook goes to this cooking school, what contract will the owner need
to offer so that the cook will exert high effort? Again, write the conditions which need
to be satisfied and draw them. Show the contract you found on the graph.
(e) (6 marks) Will the owner find it profitable to induce high effort or low effort? Will the
owner send the cook to the cooking school? Briefly explain.
Bonus Question (5 marks) Case study: Choose an economic activity and show how a
concept or theory we have studied can be used to understand what happens in that situation.
You should choose an example that we have not covered in the lectures or the tutorials. Then:
(i) introduce the economic activity that you will analyse; (ii) briefly describe the theory or
concept you will use in the case study; (iii) most importantly, apply the concept or theory
to analyse the economic activity you have chosen. Maximum word limit: 300 words.