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課程名稱︰個體經濟學
課程性質︰系必修
課程教師︰江淳芳
開課學院：社會科學會
開課系所︰經濟系
考試日期（年月日）︰11月10日
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一 是非題(20%)
1.David has utility function U(x,y)=max{x,y}. If the price of x
is the same of y,David will buy equal amounts of x and y.
2.If someone has a utility function U=1000+2min{x,y},then x and y
are perfect complements for the person.
3.Jillian spends all of her income on peaches and straberries.Peaches
are a normal good for her.Her income increased by 20 percent and
prices did not change.Her consumption of strawberries conld not have
increased by more than percent.
4.Charlies's utility function is U(x,y)=xy^2 . His marginal rate of
substitution between x and y does not change if the amount of both
goods doubles.
二 選擇題(45%)
1.Ollie has utility function U(x,y)=(x+2)(y+3).The price of x is $1 and
the price of y is $1.When he maximizes his utility subject to his
budget constraint,he consumes positive amount of both good.
Ollie consumes
a. exactly as many units of x as of y
b. 1 more unit of x than he consumes of y
c. 1 more unit of y than he consumes of z
d. 2 more unit of x than he consumes of y
e. None of the above
2.Janet consumes x1 and x2 together in fixed proportions.She always
consumes 2 units of x1 for every unit x2.One utility function that
describes her preferences is
a. U(x1,x2)=2x1x2
b. U(x1,x2)=2x1+x2
c. U(x1,x2)=x1+2x2
c. U(x1,x2)=min{2x1,x2}
e. U(x1,x2)=min{x1,2x2}
3.Twenty years ago,Dmitri cinsumed bread which cost him $10 a loaf and
potatoes which cost him $20 a sack.With his income of $330,he bought 9
loaves of bread and 12 sacks of potatoes.Today he has an income of $452.
Bread now costs him $22 a loaf and potatoes cost him $17 a sack.Assuming
his preferences haven't changed(and the sizes of loaves and sacks haven't
changed),when was he better off?
a. He was better off 20 years ago.
b. He is better off today.
c. He was equally well off in the two periods.
d. From the information given here,we are unable to tell.
e. None of the above.
4.Henri's utility function is min{x,5y+2z}.the price of x is $1,the price
of y is $15,and the price of z is $7.Henri's income is $44.How many units
of x does Henri demand?
a. 9.18
b. 11
c. 5
d. 3
e. None of the above
5.Remember the Laspeyres price index uses the old quantities for weights,
In 1991,good x cost $5 and good y cost$1.They now cost $9 and $5
respectively.In 1991 the consumption bondle was (x,y)=(4,5).The current
consumption bundle is (x,y)=(9,7).the Laspeyres index of current prices
relative to 1991 prices is closet to which of the following numbers?
a. 0.5
b. 2.4
c. 3.6
d. 1.7
e. none of the above
6.A student spends all of her income on pizza and books.When pizzas cost
$3 each and books cost $10 each,she consumed 30 pizzas and 3 books per
month.The price of pizzas fell to $2.90 each while the price of books
rose to $11 each.The price change
a. made her worse off
b. left her exactly as well off as before
c. left her at least as well off as before and possibly helped her.
d. might have helped her,might have harmrd her.We can't tell which
unless we observe what she consumed after the price change.
e. had the same effet as $3 increase in her income.
7.When the prices were($5,$1),Vanessa chose the bundle (x,y)=(6,3) .
Now at the new prices,(Px,Py),she chooses the bundle (x,y)=(5,7).For
Vanessa's behavior to be constraint with the weak axiom of revealed
preference,it must be that
a. 4Py<Px
b. Px<4Py
c. 5Py<Px
d. Py=5Px
e. None of the above
8.The absolute value of Mar's MRS at his current consumption bundle is
greater than .(That is MU1/MU2 >3).Mars has convex preferences and is
currently consuming positive amounts of both goods.
a.taking away some of good 1 and giving Mars 3 units of good 2 for each
unit of good 1 he is taken away will necessarily make him worse off.
b.taking away some of good 1 and giving Mars 3 units of good 2 for each
unit of good 1 he is taken away will necessarily make him better off.
c.Giving Mars some of good 1 and taking away 3 units of good 2 for each
unit of good 1 he is given will necessarily make him worse off.
d.Giving Mars some of good 1 and taking away 3 units of good 2 for each
unit of good 1 he is given will necessarily make him better off.
e.More than one of the above is true.
9.Georgina consumes only grapefruits and pineapples.Her utility function is
U(x,y)=x^2y^8,where x is the number of grapefruits consumed and y is the
number of pineapples consumed.Georgina's income is $105,and the price of
grapefruits and pineapples are $1 and $3,respectively.How many grapefruis
will she consume?
a. 10.5
b. 7
c. 63
d. 21
e. None of the above
三 問答題(35%)
1.(10%)
小明的所得為12元,其效用函數為U(X,Y)=XY.財貨Y的單位價格為1元,廠商提出一促銷
方案刺激消費者對X消費.此方案如下:若購買3單位以下的X,每單位2元,若購買超過3
單位的X,則前三單位仍為每單位2元,但超過3單位的部分則每單位1元.兩種財貨皆可
無限細分,所以購買時不一定要購買整數單位.
a. 請求出小明的預算限制線,並將預算線畫在XY平面上.
b. 請求出小明的最適消費
2.(15%)
小華的所得為100,他的效用函數為U(X,Y)=lnX + Y.令Px為一單位X的價格,Py為一單位
Y的價格,
a. 請推導小華對商品X的需求函數
b. 請推導小華對商品Y的需求函數
C. 當Px上升時,小華對商品X的需求會增加還是下降?
d. 當Py上升時,小華對商品X的需求會增加還是下降?對X的需求函數而言,X是否為
Y的互補品.
e. 當Px上升時,小華對商品Y的需求會增加還是下降?
3.(10%)
小英的效用函數為U(X,Y)=X+2Y,X的單價為1元,Y的單價為3元,小英的所得為12元
a. 請計算出小英的︱MRS︱ (=｜dy/dx｜)
b. 請畫出小英的預算限制式與無異曲線
c. 小英會消費幾單位的x?
d. 小英的爸爸決定每年多給小英一些零用錢,為了描述小英所得與X消費量的關係,
請畫出X產品的Engel曲線
e. 請計算X產品的所得彈性
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