推 TINTINH :已收精華區:)_ 01/12 08:24
課程名稱︰個體經濟學一
課程性質︰系必修
課程教師︰黃貞穎
開課學院：社科院
開課系所︰經濟系
考試日期（年月日）︰2010.01.11
考試時限（分鐘）：120mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. True or False: You need to explain briefly your answers.
(a) (10pts) In the CAPM model, if a stock lies strictly below the budget
line (recall that we label the standard deviation of a stock’s return on
the x-axis and the mean of that on the y-axis), then it is for sure that
no one will want to hold this stock in his optimal choice since there
is always an alternative with less risk or greater expected return.
(b) (10pts)If apples are a 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) (10pts) 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. The
consumer’s utility function takes the expected utility form.
(d) (10pts) Continue from above. Facing a risky income stream and the
expected value of the same income stream, the consumer prefers the latter
to the former.
2.Expected Utility: Suppose that a safety agency is thinking of establishing
a criterion under which an area prone to flooding should be evacuated.
The probability of flooding is 1%. There are four outcomes
(A):No flood and no evacuation is performed.
(B):No flood but an evacuation is performed.
(C):There is a flood and an evacuation is performed.
(D):There is a flood but no evacuation is performed.
Suppose that the agency is an expected utility maximizer. Suppose further
that the agency is indifferent between the sure outcome B and the lottery
of A with probability p and D with probability (1-p). Also assume that the
agency is indifferent between the sure outcome C and the lottery of B with
probability q and D with probability (1-q). Suppose it also prefers A to D
and that 0<p<1 and 0<q<1 .Let us normalize by setting the utility of getting
the sure outcome A to be 1 and the utility of getting the sure outcome D to
be 0.
(a)(10pts) Determine the expected utility of sure outcome B and the expected
utility of sure outcome C for the agency.
(b)(20pts) Consider two different policy criteria:
Criterion 1: This criterion will result in an evacuation in 90% of the
cases no matter what.
Criterion 2: This criterion is more conservative. It result in an evacuation
in 95% of the cases no matter what.
Recall that the probability of flooding is 1%. Suppose that p=0.5 and q=0.9.
Derive the probability distribution over the four outcomes under these two
criteria. Then, by using the utilities you calculate in (a), decide which
criterion
the agency will choose.
3.Consumer's surplus: A consumer has the utility function
U(x,y) =e^((ln(X)+Y)^1/3)
where X is the good in concern and Y is the money
that can be spent on all other goods. (So the price of Y is normalized to
be 1). The income of this consumer is 100.
(a) (10pts) Derive the demand function of x for this consumer. Make sure that
at every price of x, the consumer always has enough income to buy the amount
of x as indicated by hiss demand function.
(b) (10pts) Calculate the price elasticity of the demand function in (a).
Is it true that the absolute value of the elasticity of the demand decreases
as the amount of x increases?
(c) (10pts) Suppose price of x decreases from 2 to 1. Calculate the change
in consumer's surplus.
(d) (10pts) Suppose price of x decreases from 2 to 1. Calculate the
compensating variation of this price change.
(e) (10pts) Suppose price of x decreases from 2 to 1. Calculate the
equivalent variation of this price change .
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