課程名稱︰個體經濟學一
課程性質︰
課程教師︰鄭秀玲
開課系所︰
考試時間︰2006/01/12
試題 :
1.(15分) Mary's utility depends upon her income. Her utility function is
U = M^1/2
She has received a prize that depends on the roll of a pair of dice. If she
rolls a 3,4,6 or 8,she will recive $400,otherwise she will receice $100.
(1.a)What is the expected payoff from this prize? [Hint: the probability
of rolling a 3 is 1/18,the probability of rollling a 4 is 4/36, the
probability of rolling a 6is 5/36,and the probability of rolling a 8
is 5/36 ]
(1.b)What is the expected utility from this prize?
(1.c)Mary is offered an alternate prize of $169(no dice roll is required).
Will she accept the alternate prize or roll the dice?
(1.d)What is the minimum payment that Mary will accept to forego (i.e. give
up)the roll of the dice?
2.(10分) CS Metal Company produces stainless steel pots and pans. CS can
pursue either of two distribution plans for the coming year. The firm can
either produce pots and pans for sale under a discount store label or
manufacture a higher quality line for specialty stores and expensive mail
order catalogs. High initial set-up costs along with CS's limited capacity
make it impossible for the firm to produce both lines. Profits under each
plan depend upon the state of the economy. One of three conditions will
prevail: growth (probability = 0.3)
normal (probability = 0.5)
recession (probability = 0.2)
The outcome under each plan for each state of economy is given in the table
below. Figure in the table are profits measured in dollars.The probabilities
for each economic condition represent crude estimates.
Economic Condition Discount line Specialty line
Growth 250,000 400,000
Normal 220,000 230,000
Recession 140,000 20,000
(2.a)Calcute the expected value for each alternative.
(2.b)Which alternative is more riskly?(calculate the standard deviation of
profits for each alternative.)
3.(10分) The maker for tennis shoes has a horizontal supply curve and a linear
,downward-sloping demand curve. Currently the government imposes a tax of t
on every pair of tennis shoes sold and does not tax other goods. The
government is considering a plan to double the tax on tennis shoes, while
leaving other goods untaxed. If the tax is doubled ,then
a.the total deadweight loss caused by the doubled tax will be exactly twice
the original deadweight loss.
b.the total deadweight loss caused by the doubled tax will be more than
twice the original deadweight loss.
c.the total deadweight loss caused by the doubled tax will be less than
the original deadweight loss.
d.to know if doubling the tax would more than double the deadweight loss,we
would have to know the slope of the demand curve.
e.None of the above.
(單選一答案，需詳細說明如何求解)
4.(13分) Mr. Liu has an endowment of $20 each period. He can borrow money at
an interest rate of 200% ,and he can lend money at a rate of 0%.(Note:If the
interest rate is 0%,for every dollar that you save,you get back $1 in the
next period. If the interest rate is 200%, then for every dollar you borrow,
you have to pay back $3 in the next period.)
(4.a)Please illustrate his budget set in the graph.
(4.b)Mr. Liu could invest in a project that would leave him with m1=30 and
m2=15. Besides investing in the project, he can still borrow at 200%
interest or lend at 0% interest. Draw the new budget set in the graph.
Would he be better off or worse off by investing in this project given
his possibilities for borrowing or lending? Or can't one tell without
knowing something about his preferences? Explain.
5.(20分) 請分別求出以下兩函數的邊際收益函數，畫出邊際收益曲線並與其平均收益
曲線 (即inverse demand curve)做比較
(5.a)P=a-bQ ,a,b為參數
(5.b)Q=a P^e ,a 為參數 ,e為常數
6.(12分) 請以第10章所學之跨期消費選擇模型說明:
(6.a)現代年輕人與老祖母一輩的跨時期消費行為差異。
(6.b)以手上有數張信用卡的卡奴為例，說明政府施壓信用卡發卡銀行降低利率，
對這些卡奴的跨時期消費的影響為何?
7.(10分) The fundamental equilibrium condition in asset markets is that risk
-adjusted returns have to be the same.
8.(10分) 請以數學式說明下列敘述
Suppose that the demand and supply curves are both linear. If the government
imposes a quantity subsidy on a good , the amount of its price change due to
this subsidy depends on the slope of the demand and supply curves in the
market.
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