ECON3430:
MANAGERIAL ECONOMICS
Problem Set 1 (25%) Due: Monday, April 15th, 2024 at 4 pm.
Questions
Make (and state) assumptions for all questions if a good answer requires additional information.
1) Tracy is a salesperson working for PLUM autonomous drone company. The utility function of Tracy
is given by
(, , ) = + − ()
ℎ ∈ ℝ ′ ,
ℎ ,
() ′
ℎ
() = 7 < 10
() = (
1
2
× ( − 10)2) ≥ 10.
Jane is Tracy’s boss, who is maximising PLUM’s profits which are given by:
(, , ) = () − − ,
ℎ () ℎ ′
() = 200
Jane cannot observe Tracy’s effort (e) directly but observes the sales revenue R(e) and can
set the bonus payment b to depend on sales revenues.
a. Suppose Jane sets Tracy’s weekly wage to be $983 and the bonus payment b to be zero.
What would be Tracy’s effort level (e) and PLUM’s profits? (1 mark)
b. Suppose Jane sets Tracy’s weekly wage to be $83 and the bonus payment b to be $805
conditional on reaching a sales target of () = 8000 (i.e., b=0 if sales revenues are lower
than $8,000). What would be Tracy’s effort level (e) and PLUM’s profits? (1 mark)
c. Suppose Jane sets Tracy’s weekly wage to be $173 and the bonus payment to be 20% of
sales revenues (i.e. = 0.2 × ()). What would be Tracy’s effort level (e) and PLUM’s
profits? (1 mark)
d. What is the optimal wage ( ∈ ℝ) and the bonus payment b that maximises PLUM’s profits?
(2 marks)
e. Briefly discuss the potential challenges with implementing an employment contract as in d)
in a real-world setting. (2 marks)
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2) Daniel is Tracy’s work partner. Jane assigns Tracy and Daniel to work on a joint project, which can
be described as a simultaneous move game with the following payoffs:
Tracy
Work Hard Shirk
Daniel
Work Hard a, b 31, 178
Shirk 178, 31 c, d
a. Suppose a=b=150 and c=d = 50. Find the Nash equilibria of this game. (1 mark)
b. Suppose Jane wants both Daniel and Tracy to Work Hard and plans to set values for
{a,b,c,d} accordingly. What values {a,b,c,d} would ensure that both Daniel and Tracy choose
Work Hard? Interpret what such values could mean in reality. (1 mark)
c. Suppose a=179, b = 900, c= 30, d=0. In reality, why might the players not end up in the
Nash equilibrium of this game? (1 mark)
d. Modern firms increasingly assign employees to work in teams. Briefly discuss the pros and
cons of team production. (2 marks)
3) Imagine you want to buy a brand-new washing machine.
a. Search online and provide a (random) list of ten washing machine models. (0.5 marks)
b. What are the attributes of a washing machine that are most important to you? Describe
your utility function
(, , , )
where a, b, c are different attributes of the washing machine and p is the price.
(1.5 marks)
c. Reduce the number of your options from ten to three alternatives using the elimination by
aspects heuristic. Describe your process. What are the three washing machine models left
in your choice set? (1 mark)
d. For the remaining choice set with three models, show whether your preferences are
1. complete (1 mark)
2. transitive (1 mark)
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4) Suppose you own a car worth $53,000. While you have accident insurance your policy does not
provide insurance against theft. The insurance company quotes a price of an additional $159 a year
to fully insure your car against theft.
a. Suppose you are a risk-neutral expected payoff maximiser who has a good estimate of the
probability ( ∈ [0,1]) that your car might be stolen next year. At what probability p would
you be indifferent between insuring and not insuring your car against theft for a premium of
$159 a year? (1 mark)
b. How would your answer to part a) change if your preferences were characterised by
Cumulative Prospect Theory rather than Expected Utility Theory? (1 mark)
c. The insurance company also offers partial insurance that pays you 80% of the value of your
car (i.e. $42,400) in case of theft and this policy only costs $106 a year. What might be the
reason for partial insurance to be much cheaper than full insurance? (1 mark)
5) Credence goods markets
a. Define what a credence good is and explain the key characteristics that distinguish it from
other types of goods. (1 mark)
Provide an example of a credence goods market. Answer the following questions based on
this example.
b. Discuss the potential market failures that may arise in this market due to credence goods
characteristics. (2 marks)
c. Suggest two mechanisms or policies that could help mitigate the market failures in this
credence goods market. Discuss the pros and cons of each mechanism. (2 marks)