C3016. Economics of Information
Coursework 4
Problem 1 (25% of the mark of this coursework)
Recently some airlines have gone bankrupt with the effect that tourists that were on
holidays in some exotic destination could not return home with the plane ticket that
they had already purchased. They had to spend a lot of money to buy a one way ticket
to return home. The UK government is discussing whether or not to introduce a new
tax of £1 on every plane ticket sold. The money collected would be part of a fund that
would reimburse the cost of returning home to tourists if their airline were to go
bankrupt. In essence, the UK government is planning to introduce compulsory travel
insurance in case of airline bankruptcy.
Do you think that this policy initiative would increase or decrease the incentives that
customers have use airlines that are in good financial conditions? Explain why. (Max
150 words)
Give an example of other markets where the presence of insurance modifies the
incentives that customers face, and explain why. (Max 150 words)
Problem 2 (25% of the mark of this coursework)
Consider a relationship between a principal and an agent in which only two results,
valued at 50000 and 25000, are possible. The agent must choose between three
possible efforts. The probability of each of the results contingent on the efforts is
given in the following table:
Result: 25000
0.25
0.50
0.75
e1
e2
e3
Result 50000
0.75
0.50
0.25
Assume that the principal is risk-neutral and the agent is risk-averse, with their
respective preferences described by the following functions:
B(x,w)=x-w
U(x,w)=w^(0.5)-v(e)
with v(e1)=40, v(e2)=20, and v(e3)=5. The reservation utility level of the agent is 120.
(a) Write down the optimal remuneration scheme under symmetric information
for each effort level and the profits obtained by the principal in each case.
What is the optimal contract?
(b) Write down the optimal remuneration scheme under moral hazard for each
effort level. What is the optimal contract?
Problem 3 (25% of the mark of this coursework)
There are two types of workers -the industrious and the lazy. Their utility functions
are UI=w-e, and UL=w-3e respectively, where w is the payment received and e the
effort exerted. Their reservation utility is 10, independently of whether they are
industrious or lazy. The employer’s profit function is 80*(e^(0.5))-w. Assume that
effort is always verifiable. It is common knowledge that there is a fraction q of
industrious workers in the worker population.
a) Compute the optimal contracts assuming than the employer will know whether
the potential worker is lazy or industrious. Compute the employer expected
profit before she knows whether the worker will be lazy or industrious.
b) Show mathematically that if the employer offered these two contracts but she
did not know who is lazy and who is industrious then the industrious worker
would choose the contract that is intended for the lazy worker. Compute the
employer expected profit before she knows whether the worker will be lazy or
industrious.
c) Write the problem that the employer will solve to find the optimal contract if
she does not know whether the worker will be lazy or industrious
d) Discuss which restrictions are binding in the previous problem
e) Solve the problem in order to find the optimal contract
f) Compute the employer expected profit before she knows whether the worker
will be lazy or industrious, and compare them with those in parts a and b.
Problem 4 (25% of the mark of this coursework)
An employer wants to hire an employee with a utility function U=w-0.5e2, where e is
effort and w is the wage. If the employee is rich, his reservation utility is 1. If the
employee is poor, his reservation utility is 0. Both types of employees have the same
productivity equal to 2e. The employer is risk neutral, and her utility function is 2e-w.
The employer can only offer the job contract to one potential employee. The
employee can accept or reject the job. The employer obtains zero profits if the job
offer is rejected.
a) Compute the optimal contracts under the assumption that the employer knows who
is poor and who is rich (symmetric information)
b) If the employer offered the contracts obtained in (a) but she did not know who is
rich and who is poor (asymmetric information), what contract will each type of
worker choose?
c) Assume that the employer does not know who is poor and who is rich. She only
knows that a proportion q of workers is rich. Assume that the employer would like to
hire a worker for sure. What is the maximisation problem that the employer will
solve?
d) Can the employer design a contract to attract only a rich employee? If so, compute
the optimal contract under asymmetric information that attracts a rich employee only.
Compute the employer’s expected profit under that contract.
e) Can the employer design a contract to attract only a poor employee? If so, compute
the optimal contract under asymmetric information that attracts a poor employee only.
Compute the employer’s expected profit under that contract.
d) Compute the optimal contracts that solve the problem in part (c). What is the
difference in the efforts demanded under symmetric and asymmetric information?
Who obtains informational rents? Compute the employer’s expected profit.
g) Comparing (d), (e), and (f), what will the employer prefer?