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ECON30001
THE UNIVERSITY OF MANCHESTER
Advanced Microeconomics
Semester 1 2019-20
Date: 21 January 2020
Time: 09:45 – 11:15
1 HOUR 30 MINUTES
INSTRUCTIONS SPECIFIC TO THIS EXAM:
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The exam is marked out of 50.

Answer ALL questions from Part A (30 marks)

Answer ONE question from Part B (20 marks).

Electronic calculators may be used, provided that they cannot store text.

Candidates are advised that the examiners attach considerable importance to the clarity
with which answers are expressed

This paper must not be removed from the examination room
INFORMATION ABOUT THIS PAPER:

The last five pages of this exam paper have been left blank for your planning and workings.
Please note that this will not be seen by the marker, therefore will not gain you marks.
University of Manchester, 2020
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Part A: Please answer all questions (30 marks).
An employer is designing a wage contract. There are two states, ! and “. In state! revenue
is ￡400, and in state ” revenue is ￡800. If the employee exerts a high level of eVort, the
probability of state ! is 0.4. If the employee exerts a low level of eVort, the probability of
state ! is 0.8. The employee maximises expected utility, with utility for wages #($) = $.
High eVort decreases the employeeís expected utility by 6 units, and low eVort decreases it
by 1 unit. By not accepting the contract, the employee gets reservation utility of 12 units.
Question A.1: Assuming perfect information, explain and derive the contract that opti mally implements low eVort. (4 marks)
Question A.2: Assuming perfect information, explain and derive the contract that opti mally implements high eVort. (4 marks)
Question A.3: Find the optimal contract under perfect information. (4 marks)
Now assume asymmetric information, in the sense that eVort is unobservable.
Question A.4: Explain and derive the contracts that optimally implement low eVort under
asymmetric information. (3 marks)
Question A.5: Explain and derive contract that optimally implements high eVort under
asymmetric information. (10 marks)
Question A.6: Find the optimal contract under asymmetric information. (5 marks)
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Part B: Please answer ONE question (20 marks).
Question B.1: Explain the value of information in single-person decision problems and
explain why this value is never negative. Give an example (from a market or game scenario)
where the value of information is negative.
Question B.2: Explain what is meant by the ìNash solution of a two-player bargaining
game and list the axioms that characterise the Nash solution. Explain the ìdividing a dollar
bargaining game assuming two players, % and !, with utilities #! and #” that are both
strictly increasing, strictly concave, and #!(0) = #”(0) = 0. Using the Nash solution, show
that being ìmore risk averse is detrimental in this bargaining game.
Question B.3: Consider the following competitive market for insurance. There are two
states of the world: good ” and bad !. Consumers have endowment & = (&#, &”) with
&# > &”. Consumers are risk averse, expected utility maximisers, with common utility
function #. There are two types of consumers: high risk types ‘ and low risk types (. The
probabilities that ‘ and ( types nd themselves in the bad state are )$ and )%. There is
probability * that a consumer picked at random is type (. Firms are risk-neutral expected
pro t maximisers. The rm oVers consumers a state-contingent contracts + = (+#, +”)
in exchange for their endowment & = (&#, &”). Explain what is meant by a competitive
equilibrium set of contracts and characterise these contracts under asymmetric information
(assuming equilibrium exists).
END OF EXAMINATON
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