課程名稱︰個體經濟學
課程性質︰經濟系大二必修
課程教師︰鄭秀玲
開課學院：社科院
開課系所︰經濟系
考試日期（年月日）︰12/20/2007
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
以下各題均需寫出詳細推導過程(繪圖或數學式)，才予給分。
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Q1.(15分)Lisa is a widow whose primary income is provided by earnings received
from her husband's $200,000 estate. The table below shows the relationship
between income and total utility for Lisa.
_______________________
Income Total Utility
￣￣￣￣￣￣￣￣￣￣￣￣
5,000 12
10,000 22
15,000 30
20,000 36
25,000 40
30,000 42
------------------------
(1.1)Construct yhe marginal utility table for Lisa. What is her attitude
toward risk? Explain your answer including a description of the marginal
utility for individuals whose risk preferences are different from Lisa's.
(1.2)Lisa is currently earning 10% on her $200,000 in a riskless investment.
Alternatively, she could invest in a project that has a 0.4 probability of
yielding a $30,000 return on her investment and a 0.6 probability of receiving
$10,000. Should she alter her strategy and move her $200,000 to the more risky
project?
Q2.(20分) Donna is considering the option of becoming a co-owner in a business.
Her investment choices are to hold a risk free asset tha has a return of Rf and
co-ownership of the business, which has a rate of return of Rb and a level of
risk of σb. Denna's marginal rate of substitution of return for risk
(MU σp/MU Rp) is MRS Rp,σp = ∣-σp/Rp∣,wher Rp is Donna's portfolio rate of
return and σp is her optimal profolio risk. Donna's budget constraint by Rp =
Rf + (Rb-Rf)*σp/σp.
(2.1) Solve for Donna's optimal portfolio rate of return as a function of Rf ,
Rb and σb.
(2.2) Suppose the table below lists the relevant rates of returns and risks.
Use this table to determine Donna's optimal rate of return.
--------------------------------------
Investment Rate of Return Risk
--------------------------------------
Risk Free 0.06 0
Business 0.25 0.39
---------------------------------------
Q3. (15分) Mr. Kandle has a utility function c1c2, where c1 is his consumption
in period 1 and c2 is his consumption in period 2. He will have no income in
period 2. If he had an income of $80,000 in period 1 and the interest rate
increased from 10% to 19%, then
a. his savings would increase by 9% and his consumption in period 2 would
also increase.
b. his savings would not change but his consumption in perod 2 would increase
by $3,600.
c. his consumption in both periods would increase.
d. his consumption in both periods would descrease.
e. his consumption in period 1 would descrease by 19% and his consumption in
period 2 would also descrease.
(請從上述 a 到 e 單選一正確答案，需詳細說明如何求解)
Q4. (15分) Jane's preferences can be represented by U(X,Y)= min{X,Y}, where X
is bottles of milk and Y is dollars to spend on other things. She faces prices
(Px,Py)=(2,1) and her income is 12. When the price of a bottle of milk goes up
to $4, what is the maximum amount that Jane would pay to avoid the price the
price increase? In order to be as well-off as she was with her original bundle,
by what amount would Mary's original income have to rise?
Q5. (10分) 開設塑膠工廠的小楊，其工廠總資產為1000萬元，有鑑於同業常因祝融肆虐而
損失慘重，如果發生火災預計有900萬元的損失，且火災的機率為10%，因此他有意考
率投保火災險，而目前有A、B兩家保險公司向他提出保險契約，其內容如下：
A：小楊只需支付200萬元保費，但可以得到900萬元的火災理賠金。
B：小楊只要支付100萬元的保費，但指保障450萬元的火災損失。
假設小楊的貨幣效用含數為U(M) = M^1/2 (單位萬元)，試問哪個保險公司的方案對
小楊較具吸引力？
Q6. (15分) 假設某學生下課後的主要敲淺微看錄影帶(X)與打電腦遊戲(Y)，假設該學生扣
生活所需後的可支配所得為60美元，每套錄影帶的租金為5美元，電腦遊戲每套為10
美元，其對這兩種休閒活動的效用函數為 U = f (X,Y) = X^1/3Y2^3，請問：
(6.1) 假設因影帶版權費調漲，使得錄影帶租金也急遽攀升至每套10美元，該留學生的消
費選擇為何？
(6.2)承第(6.1)題，價格上升對該留學生租錄影帶的替代效果、所得效果與總效果為何(
以 Slutsky 定義 real income 不變)？
Q7. (10分)請繪圖並說明 "The Slutsky and Hicks demand curves are always
downward sloping curves. The ordinary curve is a downward sloping curve for
normal goods but is upwards for an giffen good."
加分題 (5分)：
讀完「11件事人生中必做的事，張忠謀線上告訴你」一文後，你認為自己需要再加強哪方
面的學習？該文中有您不認同之處嗎？
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