Question 1 (300 Words Maximum)
An individual’s indirect utility function is defined as the following:
?2
?1?2
where ?1 and ?2 represent the prices of goods 1 and 2, respectively, and ? denotes
individual income.
a) Outline the general properties associated with the indirect utility function and
describe an application where the indirect utility function is useful from a
policy perspective.
b) State and prove Roy’s Identity. Use your result to derive the Marshallian
demand functions for goods 1 and 2.
Question 2 (300 Words Maximum)
a) Show that, if offered at a fair premium, a risk averse individual will choose
to fully insure.
b) In the context of asymmetric information, outline the problems in offering
insurance contracts.
Question 3 (300 Words Maximum)
An individual has zero initial wealth and is offered the following two prospects:
Prospect 1: A: (4,000, 0.80) or B: (3,000)
Prospect 2: C: (4,000, 0.20) or D: (3,000, 0.25)
a) Most individuals choose B in problem 1 and C in problem 2. Show this
behaviour is inconsistent with expected utility theory and intuitively explain how
prospect theory can account for this behaviour.
b) Sheffield University United are losing a football match 3-0 at half time. In the
second half they start to play less conservatively (that is, take increased risk
with their decisions) compared to the opposition team. Explain whether this
behaviour is consistent with prospect theory.
Question 4 (300 Words Maximum)
Suppose a decision maker faces the following two intertemporal decision problems. In
both problems the decision maker has to choose in which period they would prefer to
receive a payment. They have to make both decisions in period t=1.
Problem 1: Option A: Receive 500 in t = 1 or Option B: Receive 600 in t=2
Problem 2: Option C: Receive 500 in t = 2 or Option D: Receive 600 in t=3
a) Evidence shows that decision makers tend to choose Option A in Problem 1
and Option D in Problem 2. Suppose that the discount factor is δ, is this
behaviour consistent with exponential discounting?
b) Intuitively explain the β-δ model of hyperbolic discounting and discuss whether
this model is consistent with the behaviour above.
Section B (Total words: 1800)
Please answer 1 question in this section
1) Outline the key differences between prospect theory and expected utility theory.
With reference to the empirical literature, critically evaluate whether prospect
theory overcomes the observed violations of expected utility theory.
2) Outline the key differences between the discounted utility model and the model
of hyperbolic discounting. With reference to the empirical literature, evaluate
the empirical evidence for time inconsistent behaviour and discuss any
interventions which may correct this behaviour.