課程名稱︰個體經濟學一
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）︰2009/1/12
考試時限（分鐘）：140
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一選擇題(20%)
1.The demand for tickets is given by D(p)=200,000-10,000p,where p is the
price of tickets.If the price of tickets is$8,then the price elasticity
of demand for tickets is
a. -0.33
b. -1.33
c. -1
d. -2
e. -0.67
2.The demand for cable television hookus is Q=100-10p^0.5+2I^2,where P
is price and I is per capita income.Cable TV is
a. a normal good.
b. a natural monopoly
c. an inferior good
d. a substitute good
e. a complement good
3.Bernice's preferences can be represented by the utility funcion,
U(x,y)=min{x,y}.She faces prices($2,$1),and her incomes is $12.If prices
change to ($3,$1),the compensating variation
a. equals the equivalent variations.
b. is $2 greater than the equivalent variation.
c. is $2 smaller than the equivalent variation.
d. is $1 greater than the equivalent variation.
e. There is not enough information to determine which variation is larger.
4.Sally is an expected utility maximizer with utility function
pu(c1)+(1-p)u(c2),where for any x<7,000,u(x)=2x,and for x greater than or
equal to 7,000 u(X)=14,000+x.
a.Sally will be risk averse if her income is less than$7,000 but risk loving
if her income is more than $7,000.
b.Sally will be risk neutral if her income is less than $7,000 and risk averse
if her income is more than $7,000.
c.Sally will never take a bet if there is a chance that it leaves her with
wealth less than $14,000.
d.For bets that involve no chance of her wealth exceeding $7,000 ,Sally will
take any bet that has a positive expected net payoff.
e.None of the above.
問答題(80%)
1.(10%)
Charlie's utility function is XAXB.The price of apples used to be $1,the price
of bananas used to be $2,and his income used to be $40.Now the price of apples
increases to $5 and the price of bananas stayed constant,
a.How many apples did Charlie consume before the price change?
b.Please calculate the substitution effect.
2.(10%)
Ethel is trying to decide whether to have 0 car,1 car,2cars.If x is the
number of cars she has and y is the amount of money she has per year to spend
on other stuff,Ethel's utility function is U(x,y),where U(0,y)=y^1/2
U(1,y)=(15/14)y^1/2,and U(2,y)=(10/9)y^1/2.Suppose that it costs$2,000 a year
to have 1 car and$4,000 a year to have 2 cars.Ethel finds that the right thing
to do depends on her income.
a.What is her willingness to pay for 1 car if her income is M?
b.What is the lowest income at which she would have a car?
3.(10%)
The inverse demand function for grapefruit is defined by the equation
p=145-6q,where q is the number of units sold.The inverse supply function is
defined by p=5+4q.A tax of $20 is imposed on suppliers for each unit of
grapefruit that they sell.
a.Before the tax implement,what is the price of grapefruit in the equilibrium?
b.Please calculate the consumer surplus before and after the tax.
c.What is the deadweight loss(excess burden)in this case?
4.(15%)
In an isolated peasant village,the only crop is corn.Good harvests alternate
with bad harvests.This year the harvest will be 1,000 bushels.Next year it
will be 150 bushels.There is no trade with the outside world.Corn can be
stored,but rats will eat 25%of what is stored in a year.The villagers have
the Cobb-Douglas utility function U(c1,c2)=c1c2,where c1 is consumption this
year and c2 is consumption next year.
a.Draw a budget line for the village with this year's consumption on the
horizontal axis and next year's consumption on the vertical axis.on your graph
show the quantities at which the budget line intercepts the vertical and
horizontal axes.
b.How much will the villagers consume this year?
c.How much will the rats eat?
d.How much will the villagers consumer next year?
5.(15%)
Ernie's wage rate is$10 an hour.He has no earnings other than his labor income.
His utility function is U(C,L)=CR^2,where C is the amount of money he spends on
consumption,and R is the number of hours a day he spends not working.
a.Write an equation that describes Ernie's budget constraint.
b.How many hours does Ernie choose to work per day?
c.How much money does he spend on consumption per day?
6.(10%)
The certainty equivalent of a gamble is defined to be the amount of money which,
if you were promised it with certainty,would be indifferent to the gamble.
a.If an expected utility maximizer has a von Neuman-Morgenstern utility funtion
U(W)=W^1/2 (where W is wealth)and if the probability of events 1 and 2 are both
1/2,write a formula for the certainty equivalent of a gamble that gives you x
if event 1 happens and y if event 2 happens.
b.Generalize your formula in part (a)to the case where probability of event 1
is p and the probability of event 2 is 1-p.
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