推 TINTINH :已收精華區:) 01/17 10:10
課程名稱︰個體經濟學一
課程性質︰經濟系必修
課程教師︰陳添枝
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰2010.1.14
考試時限（分鐘）：180mins
是否需發放獎勵金：YES
（如未明確表示，則不予發放）
試題 :
Help: √2=1.414, √3=1.732, √5=2.236, √7=2.646, √10=3.162
1.(12 points) Larry Winters makes decisions under uncertainty based on the
following expected utility function:
U(c_1,c_2)=π_1v(c_1)+π_2v(c_2),
where v(c_1)=√c_1, v(c_2)=√c_2; c_1, c_2 are consumptions
at state 1 and state 2, and π_1, π_2 are probabilities of
respective states.
When Larry is about to graduate from the university, he is
offered two jobs: Company A offers him a fixed annual salary
of 360,000NT, company B offers him an annual salary of 300,000NT,
plus a bonus of 150,000NT if the company's products are
successful. No bonus will be given if the products fail. Suppose
the probability for the products to succeed is 50%, will Larry
take the offer from company A or B? At what probability of
product success will the two offers be equally attractive?
2.(12 points) Larry Winters has a utility function as shown in question 1. He
has a nice house worth $500,000. If typhoon hits the town, the
house will be damaged by $50,000, with a value of $450,000
remaining. The probability of typhoon is 10%. Larry can purchase
an insurance against typhoon for an amount he chooses, up to
$500,000 of course. Suppose the insurance company charges a
premium of 10% on the insurance policy. That is, if he purchases
x amount of insurance, he has to pay 0.1x as the premium no
matter what happens; the insurance company will pay him x in the
event of typhoon. Will he purchase any insurance? If yes, how
much? (Hint: treat two states of consumption as two commodities
and maximize his utility by equating MRS to relative price of
two commodities.)
3.(10 points) Taiwan government offers a lottery to its people. The price of
lottery ticket is 100NT. The prize is 1,000,000NT; however, the
probability of winning the prize is less than 1/10,000. Many
people purchase the tickets despite the fact that the expected
value of the lottery is less than its price. Could you use a
risk-lover's utility function to explain this phenomenon?
4.(10 points) There are two assets on the market. Asset A offers a mean return
of 5% and a standard deviation of 5%; asset B offers a mean
return of 10% and a standard deviation of 10%. If you ask Larry
Winters, who is risk averse, to choose between A and B, he would
prefer A. However, he decides to divide his wealth between a
risk-free asset (bank deposit) and asset B; no money is invested
in asset A. Please explain why this is possible? (Hint: use the
mean-devariance model to explain the portfolio choice.)
5.(15 points) The demand and supply function are given below:
Demand: P=30-0.2Q
Supply: P=10+0.2Q
(1) Find the equilibrium price and quantity.
(2) If the government imposes a tax of 2NT on each unit of good sold
and the suppliers are obligated to pay the tax. What would be
the equilibrium price and quantity? (Hint: as a result of tax,
the price that suppliers are willing to accept at any quantity
increases by 2.)
(3) Calculate the effects of tax on consumer surplus and producer
surplus. Also calculate the tax revenue. Are the losses in
consumer surplus and producer surplus offset by tax revenue?
6.(14 points) The utility function is given by u(x,y)=xy, where x, y are the
only two commodities to be consumed. Income of the consumer is
120.
(1) Calculate the demand for x and y if the prices are Px=5, and
Py=10, respectively.
(2) If the price of x increases from 5 to 6, price of y remains the
same at 10, what would be the demand for x and y? Please
calculate the compensation variation (CV) and equivalent
variation (EV) for the price change.
7.(12 points) The utility function is given by u(x,y)=xy, where x, y are two
commodities to be consumed. Income of the consumer is m, and
prices of x and y are Px and Py respectively.
(1) Please calculate price elasticity for x and y when m=120, Px=5,
Py=10. If Px changes from 5 to 10, while m and Py are unchanged,
what will be the price elasticity for x and y?
(2) Please calculate income elasticity for x and y when m=120, Px=5,
Py=10. What will happen to income elasticity if income is 130
rather than 120?
8.(15 points) Consumer A's inverse demand function for a good is given by
P=20-0.5Q
(1) If there are five consumers and all have the above demand
function, what is the aggregate demand?
(2) What is the quantity demanded by the entire market when P=5?
Calculate price elasticity and marginal revenue at this point.
(3) At what price will the revenue be maxmized?
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