課程名稱︰個體經濟學二
課程性質︰必修
課程教師︰江淳芳
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰2013/06/20
考試時限（分鐘）：9:20-12:00
試題 :
Microeconomics Final Exam Time: 9:20-12:00
1. (7%) Consider a market of risk-averse decision makers, each with a utility
function U = √I. Each decision maker has an income of $900,000, but faces the
possibility of a loss of %50,000 in income. Each decision maker can purchase an
insurance policy that fully compensates her for her loss. This insurance policy
has a cost of $5,900. Suppose each decision maker potentially has a different
probability q of exeriencing the loss.
(a) What is the smallest value of q so that a decision maker purchases
insurance?
(b) What would happen to this smallest value of q if the insurance company were
to raise the insurance premium from $5,900 to $27,500?
2. (7%) The village of Sky Fall has 700 residents. They have a single public
good, the happy farm. Everyone's utility function is U_i(X_i,Y) = X_i - 121/Y,
where X is the amount of money spent on private consumption, and Y is the size
of the happy farm in square meters. The cost of the happy farm is $7 per square
meter. Everyone has an aincome of $5,000. What is the Oareto efficient size for
the happy farm?
3. (20%) Suppose that Robinson and Friday have the following production
possibility frontiers for good x and good y.
Robinson: x^2 + y^2 = 100,
Friday : x^2 + y^2 = 100, x,y ≧ 0
Their preferences for good x and good y can be expressed as :
Robinson: u = xy^2,
Friday : u = x^2y
Please answer the following question:
(a) Robinson is in Happy Island alone. He has to produce x and y for himself.
How much units of good x and good y will he produce?
(Hint: The MRT = x/y for the production possibility frontiers x^2 + y^2 = k)
(b) Both Robinson and Friday are in Happy Island. But both of them are sick and
cannot produce anything. Fortunately Robinson finds 8 good x and 10 good y on
the ground and Friday finds 8 good x and 4 good y on the ground. Is this
allocation Pareto efficient? Can you come up a way to improve their welfare?
(c) Both Robinson and Friday are in Happy Island. They are health and are able
to produce good x and good y. Robinson decides to produce 6 units of good x and
8 units of good y. Friday decides to purduce 8 unit of good x and 6 units of
good y. They will exchange to improve their utilities after production. Is
their production plan efficient? Can you come up a way to improve their
welfare?
(d) In the general equilibrium, will Robinson be the seller of x? Explane why.
4. (24%) The town of Steeleville has three steel factories, each of which
produces air pollution. There are 10 citizens of Steeleville, each of whose
marginal benefits from reducing air pollution is represented by the curve
P(Q) = 5 - Q/10, where Q is the number of units of polutants removed from the
air. The reduction of pollution is a public good. For each of the three source
of air pollution, the following table lists the current amount of pollution
being produced with the constant marginal cost of reducing it.
Units of Pollution MC of pollution
Source Currently Being Produced Reduction
──────────────────────────
Factory A 20 $10
Factory B 40 $20
Factory C 60 $30
(a) On a graph, illustrate marginal benefits ("demand") and the marginal costs
("supply") of reducing pollution.What is the efficient amount of pollution
reduction? Which factories should be the ones to reduce polution, and what
would the total costs of pollution reduction be? In a private market, would and
units of this public good be provided?
(b) The Steeleville City Council is currently considering the following
policies for reducing pollution:
i. Requiring each factory to reduce pollution by 10 units.
ii. Requiring each factory to produce only 30 units of pollution.
iii. Reequiring each factory to reduce pollution by one fourth.
Calculate the total costs of pollution reduction associated with each policy.
Compare the total costs and amount of pollution reduction to the efficient
amount you found in part (a). Do any of these policies creat a deadweight loss?
(c) Another policy option would create pollution permits, to be allocated and,
if desired, traded among the firms. If each factory has a permit allowing it to
produce 30 units if pollution, which factories, if any, would trade them?
(Assume zero transactions cost.) If they do trade, at what prices would the
permits be traded? How does your answer in part (c) relate to in part (a)?
5.(18%) Suppose that low-productivity workers all have marginal products of 6
and high-productivity workers all have marginal products of 12. The community
has equal numbers of each type of worker. The local community college offers
four-year college education. The cost of college education for a
high-productivity worker is 1 and the cost of college education for a
low-productivity worker is 2. The reserve utility (the utility of no working
and no education) is 0 for all workers.
(a) Will there be a separating equilibrium? Please describe the choices made by
firms and workers in the equilibrium. Explain.
(b) Suppose now the reserve utility is 10 for high-productivity workers. Please
describe the choices made by firms and workers in the equilibrium.
(c) Suppose now the reserve utility is 10 for high-productivity workers, and
the local college offers a training program. High-productivity worker think
finishing the program is as bad as a wage cut of 5. Will there be a separating
equilibrium? Please describe the choices made by firms and workers in the
equilibrium. Explain.
6. (24%) There are two types of drivers in an island: careless drivers and
careful drivers. A careless driver's car will be stolen with probability 0.5.
A careful driver's car will be stolen with probability 0.2. Geico, a car
insurance firm, cannot distinguish between careless drivers and careful
drivers. The CEO of Geico designed two insurance policies. Policy A offers fair
insurance for careful drivers(i.e., the premium rate is 0.2) and policy B
offers fair insurance for careless drivers(i.e., the premium rate is 0.5). Both
can be purchased in unlimited quantities.
Tom is a careless driver/ His utility function of consumption is u(c) and he is
risk averse. Without insurance, Tom has $1,000 worth of assets (C_g = 1,000) if
his car is not stolen and has $250 worth of assets (C_b = 250) if his car is
stolen. Tom's indifference curves over C_g and C_b can be depicted in the
following graph.
Graph: http://ppt.cc/Ci7z
(a) (4%) Please write down Tom's expected utility function. Please derive the
MRS when C_g = C_b.
(b) (4%) Please plot the budget line associated with the purchase of insurance
policy A and the budge line associated with the purchase of insurance policy B
on a graph.
(c) (4%) If policy A is not available, how much insurance will Tom buy?
Explain.
(d) (4%) When both policy A and policy B are both available, which policy will
Tom choose? What type of information problem does the insurance company face?
(e) (8%) Now a new CEO would like to solve the infomation problem. The new CEO
decides to keep policy B unchanged, but add a limitation in policy A: in policy
A, the pruchase amount of insurance cannot be exceed X. Will the change be able
to solve the information problem? If so, how should the new CEO decide X?