Economic of Business Contracts and Governance Worksheet

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ECON 4007 ECONOMICS OF BUSINESS: CONTRACTS AND GOVERNANCE
2020/21
IN-COURSE EXAM PAPER
STUDENTS ARE REQUIRED TO SOLVE ONE EXERCISE
EXERCISES CARRY EQUAL WEIGHTS.
Exercise 1:
a) The utility functions of two individuals are
??1 = 20(??1 + ??2 ) ? 15??1 and ??2 = 10(??1 + ??2 ) ? 15??2 ,
where ??1 is the effort contributed by individual 1 and ??2 is the effort contributed by
individual 2. Each individual ?? can set ???? equal to any number between zero and one
inclusive.
Derive the best responses of individuals. Justify your answer
What is the Nash equilibrium of this game? Explain your answer and give an intuitive
explanation of the derived equilibrium.
[33%]
b) Laura’s utility-of-wealth function is ??(??) = 1 ?
1
. Her current wealth is £100. There
??+1
is a probability of 0.2 that £60 of her wealth will be destroyed in an accident. Insurance
can be purchased for 0.40 pounds per pound of coverage.
Derive the market opportunity line. Does it represent fair odds? Explain.
How much insurance coverage will Laura purchase? What will Laura’s wealth be if she
has an accident, and what wealth will she have if she does not have an accident?
Is Laura fully insured? Explain. If not, derive the price per pound of coverage that
assures that aura is fully insured.
[33%]
4
Continued overleaf
c) Suppose that there is a competitive insurance market with a large population of
identical individuals. Suppose that everyone has an endowment time of ?? = 1. If an
individual devotes ?? units of effort to preventive care then the probability of an accident
is 1 ? ??. Everyone has the expected utility function:
??(??)(0.2???) + (1 ? ??(??))(0.2???) + ?? ? ??,
where ??(??) is the probability of an accident when ?? units of effort to preventive care
are supplied, ?? represents individual wealth if there is an accident, and ?? represents
individual wealth if there is no accident. If the individual is not insured, then ?? = 50 is
the individual wealth if there is an accident and ?? = 150 is the individual wealth if there
is no accident.
Assuming that the values of ?? and ?? are determined in a competitive insurance market
with fair odds, show how ?? depends on ??, that is, ?? (??).
Find the value of ?? that maximize per capita expected utility when the individual gets
?? (??) if there is an accident and ??(??) if there is no accident. By using a calculus-based
explanation, explain why the competitive equilibrium is inefficient.
[33%]
5
Continued overleaf
Exercise 2:
a) Consider an economy that produces electricity by burning coal, discharging sulphur
dioxide into the air in the process. Suppose that the government wants one of the
firms to reduce its output of sulphur dioxide by 20%, and it is going to choose the
firm in the economy that can do so at lowest cost. The true adjustment cost of each
firm in the economy is given by the table below:
Firm:
Adjustment Cost:
1
100
2
110
3
120
Suppose that the government knows that there are three firms in the economy, but it
does not their true adjustment costs.
To elicit the true adjustment costs the government employs a mechanism which has
the following features:
• Each firm must report an adjustment cost.
• The firm announcing the lowest adjustment cost will be forced to implement the
reduction of sulphur dioxide.
• The firm announcing the lowest adjustment cost is paid the second-lowest cost,
and all other firms are paid 10% of the lowest reported cost.
Determine whether a firm can ever profit by deviating from truth-telling. Explain your
answer.
Propose a mechanism that induces each firm to report its adjustment cost truthfully.
Explain your scheme from the standpoint of each firm in the economy.
[33%]
6
Continued overleaf
b) Three individuals (call them 1,2 and 3) have jointly inherited five assets (call them
A, B, C, D and E). It is left to the heirs to allocate the assets among themselves.
Therefore, the feasible outcomes are the different assignments of the assets to the
three individuals. The individual preferences are as follows:
Individual 1 strictly prefers A to B, B to C, C to D, and D to E.
Individual 2 strictly prefers E to D, D to C, C to B, and B to A.
Individual 3 is indifferent between each pair of assets.
Everyone derives positive utility from each asset.
List five efficient outcomes that leave individual 3 with nothing.
List five efficient outcomes that leave individual 2 with nothing.
List five efficient outcomes that five each individual at least one asset.
[33%]
c) Tanya’s utility-of-wealth function is ??(??) = ln?(?? + 1). Her current wealth is £100.
There is a probability of 0.2 that £60 of her wealth will be destroyed in an accident.
Insurance can be purchased for 0.25 pounds per pound of coverage.
Derive the market opportunity line. Does it represent fair odds? Explain.
How much insurance coverage will Tanya purchase? What will Tanya’s wealth be if
she has an accident, and what wealth will she have if she does not have an accident?
Is Tanya fully insured? Explain. If not, derive the price per pound of coverage that
assures that Tanya is fully insured.
[33%]
7
End of paper
x2
2
A risk neutral manager has utility function u(x, y) = 50x + y, where x is the amount of
leisure consumed and y is labour income. The manager is endowed with T = 24 of x and zero
units of y. The manager’s best alternative opportunity provides a level of utility of uy = 624. If
the manager supplies e units of efforts then the firm profit R will be 30e + }, where & is a
random variable with expected value zero. R is profit before deducting the manager’s pay.
Suppose that the owner of the firm offers the manager the compensation contract y = OR + F,
where 0 Sos 1 and F is a constant. Derive the manager’s effort supply function. Show that
effort increases when 0 increases.
Derive the optimal contract that maximizes the owner’s expected profit by employing
the manager’s effort supply function
What is the owner’s expected profit, the manager’s expected utility and the effort
supplied by the manager under the contract that maximises the owner’s expected
profit?

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Explanation & Answer:
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business

economics

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