推 fxm20689 :QQ 第3題沒看熟 寫錯了 10/27 00:38
課程名稱︰個體經濟學一
課程性質︰必修
課程教師︰黃貞穎
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰991025
考試時限（分鐘）：原90，後延至120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Answer all questions. There are 130 points in total. Good luck.
1. Every weekend, Eliette goes to an amusement park (FunLand) and spends her
entire budget of $40. There are only two things she spends her money on
there: roller coaster cost $3/ride and ice cream cost $2/cone, Eliette buys
8 rides and 8 cones.
(a)(10 points) In week 2, the FunLand changes its price to $2/ride and
$3/cone. Is it possible for Eliette to be strictly worse off? Is it
possible for Eliette to be strictly better off? Could she be exactly as
well off as before (indifferent)? Explain.
In week 3, FunLand changes its prices back to $3/ride and $2/cone (the same
as in week 1). But a new amusement park, Bob's wonderland, opens. At Bob's
wonderland, roller coaster rides and ice cream cones both cost $2. If
Eliettewent there, she would buy 15 rides and 5 cones. To compete, FunLand
offers the following promotion: any customer who spend at least $40 will get
$15 worth of free coupons to spend on either roller coaster rides or ice
cream cones.
(b)(15 points) Would Eliette rather go to FunLand or to Bob's wonderland?
Explain.
2. Your TA has utility over books (B) and movie tickets (M) as follows:
u(B,M) = B + lnM .
The price of books and movie tickets is pB=pM=1 and the income devoted by
TA to these goods is 4.
(a)(10 points) What is the TA's consumption of B and M?
(b)(15 points) Imagine that I dicide to give 2 movie tickets to your TA for
free. These coupons connot be resold. In a clearly labeled diagram (label
M on the x-axis and B on the y-axis), show your TA's budget set in this
situation. Indicate your TA's chosen consumption of M and B.
(c)(20 points) Your TA wants to save me money. So he proposes a deal to swap
movie tickets for book coupons. Each book coupon allows your TA to buy
one book. In doing so, he tries to keep himself as well off as before in
(b) but at the same time save me the maximum possible amount of money.
How many book coupons will your TA want to swap? How many book coupons
will your TA demand in exchange for the movie tickets? (Note: Tickets and
Coupons do not have to be traded in whole nunbers.)
(d)(20 points) Your TA is smart. So he proposes a deal to swap movie tickets
for book coupons. Each book coupon allows your TA to buy one book. In
doing so, he tries to keep me sending the same amount of money as in (b)
but at the same time make himself as better off as possible. How many
book coupons will your TA want to swap? How many book coupons will your
TA demand in exchange for the movie tickets? (Note: Tickets and Coupons
do not have to be traded in whole nunbers.)
3. (20 points) A consumer spends his daily income of 200 on bread (X) and milk
(Y) which cost 50 per unit. His preferences can be dscribed by the utility
function U(X,Y)=XY. In a clearly labeled diagram, draw his price offer
curve for bread.
4. (20 points) John consumes only milk and cookies. You observe John's demand
function for milk is x=10-p (where p is the price of the milk, x is the
quantity demanded of milk) when his income is 100 and the price of cookies
is 4. John's preference is monotonic. Derive John's demand function for
milk when his income is 200 and the price of cookies is 8. (Hint: when price
and income are doubled, the optimal consumption stays the same.)
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