代写 ECON301 ADVANCED MICROECONOMICS

ECON301

ECON301

ADVANCED MICROECONOMICS

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

代写 ECON301 ADVANCED MICROECONOMICS

代写 ECON301 ADVANCED MICROECONOMICS

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

代写 ECON301 ADVANCED MICROECONOMICS

代写 ECON301 ADVANCED MICROECONOMICS