代写 ECON301 ADVANCED MICROECONOMICS

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    • 代写 ECON301 ADVANCED MICROECONOMICS

    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
     
    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