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ECON301
ASSIGNMENT 1
DUE 4PM FRIDAY 15 APRIL 2016
(1) Consider the following exchange economy with 2 consumers and 2 goods.
u 1 (x 1
1 ,x
1
2 ) = x
1
1 x
1
2 + 4x
1
1
e 1 =
? 3
2 ,0
?
u 2 (x 2
1 ,x
2
2 ) = lnx
2
1 + lnx
2
2
e 2 =
? 1
2 ,4
?
.
(a) Draw an Edgeworth Box diagram to summarise the information above.
[5 marks]
(b) Identify the set of Pareto efficient allocations for this economy.
[10 marks]
(c) Identify the core of this economy.
[5 marks]
(d) Suppose the allocation is determined using markets and each consumer acts as
a price-taker. What is the equilibrium price ratio
p 1
p 2
and associated Walrasian
equilibrium allocation?
[10 marks]
(e) Suppose instead the endowments were
e 1 =
? 1
2 ,0
?
and e 2 =
? 3
2 ,4
?
.
Explain how your replies to (a) – (d) would change.
[15 marks]
(2) Consider a risk-averse expected utility maximiser with total wealth of \$50,000, including
a car valued at \$30,000. There is a probability
1
10

that she has an accident after which
her car is worthless. A risk-neutral insurance company offers insurance on the following
terms. Any amount of cover up to \$30,000 can be purchased against losses from having
an accident at a premium of ρ per dollar of cover. Let c denote the level of cover chosen
by the consumer. Hence, she can choose any c ∈ [0,\$30,000], i.e., 0 ≤ c ≤ \$30,000. She
pays a total of \$ρc for the policy and receives \$c from the insurance company if she has
an accident.
(a) Draw a Hirshleifer-Yaari diagram to depict the set of insurance options available
to this consumer (her “budget line”). This is the set of state-contingent wealth
vectors she can achieve by purchasing different levels of cover. Be sure to carefully
label your diagram and to explain how you constructed the “budget line”.
[12 marks]
(b) Using your diagram, explain under which condition this consumer will choose c =
\$30,000.
[12 marks]
(c) Assume that full insurance induces risky behavior: If the consumer has full insur-
ance, she speeds, which increases the risk of an accident. Explain how this may
destroy the market for full insurance.
[6 marks]
1