推 hsuzchan : 已收入經濟系 ＝） 01/27 14:23
課程名稱︰個體經濟學一
課程性質︰經濟系大二必修
課程教師︰黃貞穎
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰106年1月9日
考試時限（分鐘）：180分鐘
試題 :
1.
Tom has an initial wealth of 100. His car may be stolen so he runs a risk of a
loss of 40 dollars. The probability of loss is 0.2. It is possible, however,
for Tom to buy insurance. One unit of insurance costs γ dollars and pays 1
dollar if the loss occurs. Thus, if α units of insurance are brought, the
wealth of Tom will be 100-γα if there is no loss (a good state) and
100-γα-40+α if the loss occurs (a bad state). Tom is an expected utility
maximizer with Bernoulli utility function u(x)=ln(x) where x is his wealth in
a state.
(a)(10%)
Write down Tom's expected utility if he buys α units of insurance. Different-
iate it with respect to α to derive the first order condition which will be
useful later.
(b)(10%)
Suppose in 2016 insurance is actuarially fair in the sense that the insurance
company breaks even on average. What should γ be? How much insurance (α)
will Tom buy? What is his wealth in the good state? What is his wealth in the
bad state? Does Tom face any risk after being insured?
(c)(10%)
In 2017 insurance company decides to change the premium so now γ becomes 0.25
How much insurance (α) will Tom buy now? What is his wealth in good state?
What is his wealth in the bad state?
(d)(10%)
Facing the premium change from 2016 to 2017, what is the Slutsky substitution
effect of Tom's wealth in the good state?
2.
Consider a consumer who lives for two periods. The consumer gets utility from
consumption in each period. The consumer also gets an endowment of time in
each period, L hours, which the consumer can use to work or consume as leisure
. The consumer gets NO utility from leisure, however. There is no borrowing or
lending.
(a)(10%)
Let w1 and w2 be the wage rates per hour in periods 1 and periods 2 respect-
ively. In period 1, the consumer can spend some of the time endowment of
obtaining education. Call this amount of time h. This time provides neither
utility nor disutility, but it reduces the time available for working. The
benefit of spending time on education is that this raises the wage the
consumer can earn in period 2. In particular, assume
w2=h．w1
Under these assumptions, draw the intertemporal budget set of the consumer.
(b)(10%)
The consumer's utility function is
u(c1,c2)=lnc1+βlnc2
where c1 is the consumption of period 1, c2 that of period 2 and β>0 a
constant. Write down the optimization problem this consumer faces and solve
for the optimal h of this consumer.
(c)(10%)
What effect does an increase in β have on the decision to invest in eduction?
Interpret.
3.
True or False: You need to explain briefly your answers.
(a)(10%)
In the CAPM model, if stock A has the same standard deviation of return as
stock B, and has lower expected return than stock B, then no one would want to
hold stock A because all money invested in stock A should go to stock B.
(b)(10%)
If apples are normal good for a net supplier of apples, then it is possible
that when the price of apples increases, his demand for apples increases as
well.
(c)(10%)
Suppose there are two states of nature. State 1 occurs with probability p1 and
state 2 with p2 = 1-p1. A consumer has the utility function of the following
U(c1,c2,p1,p2) = c1^p1．c2^p2
where c1 is his consumption at state 1 and c2 is that at state 2. Since the
consumer is behaving exactly like an expected utility maximizer who has the
utility p1．ln(c1)+p2．ln(c2), we claim that the consumer's utility function
takes the expected utility form.
Enjoy the winter break!
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