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課程名稱︰個體經濟學一
課程性質︰經濟系大二必修
課程教師︰黃貞穎
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰97/11/11
考試時限（分鐘）：120mins
是否需發放獎勵金：y
試題 :
1.There are only two goods in this world, apples and oranges. Denote the price
of apples by Pa and that of oranges by Po. Denote a consumption bundle of x
units of apples and y units of oranges by (x,y).
John in Taipei is an utility maximizer. You observe that when Pa = 2 and Po = 1
and his income is 100 , his unique optimal choice is (25,50). Over a short
period of time when his preference should be quite stable , you further observe
that: when Pa = 1 and Po = 1 ,and his income is 100, his unique optimal choice
is (50,50) ; when Pa = 1 and Po = 1 ,and his income is 75 ,his unique optimal
choice is (37.5,37.5)
(a)(20%) Decompose the total effect in apples into Slutsky substitution effect
and income effect when the price of apples changes from 2 to 1 , the prices of
oranges stays at 1 and John's income stay at 100.
John in Kaohsiung is another utlity maximazer. You observe that when Pa = 3
and Po = 1 and his income is 60 , his unique optimal choice is (10,30). Over
the same short period of time when his preference should be quite stable , you
further observe that: when Pa = 1 and Po = 1 ,and his incomeis 60 , his unique
optimal choice is (30,30); when Pa = 1 and Po = 3 ,and his income is 60 ,his
unique optimal choice is (30,10).
(b)(20%)We say that John in Taipei and John in Kaohsiung have the same
preference if their prefernces are exactly the same so that whenever one weakly
prefers a bundle to another bundle , so will the other and vice versa. From
the data given you above , can you make a logical inference on whether it is
possible that John in Taipei and John in Kaohsiung have the same preference?
If you answer is positive,briefly explain why and make am educated guess about
what their preference could be. If your answer is negative , briefly argue why
it is impossible that they have the same preference.
2. Andrew loves to watch baseball games and play piano in his free time. To
watch a baseball game ,you need to buy the game ticket and hotdogs (it is not
a ballgame without hotdogs I can assure you). Therefore , each ball game costs
Andrew 20 dollars. Typically , each ball game lasts for 2 hours. Andrew does
not have a piano at home nearby. Hence to play piano , he has to go to a
private lesson which costs 40 dollars per hour. Andrew is a wealthy professor,
so he can spend as much as 200 dollars per week for his hobbies (ball games and
piano lessons). However , since he is a chair in his department , he does not
have much free time. Each week he has only 8 hours of free time at the most.
Each week he has only 8 hours of free time at the most. In the following ,
assume that ball games and piano lessons can be consumed in continuous amounts
and always put the number of hours of piano lessons on the x axis and the
number of ball games on the y.
(a) (20%) Draw all the possible consumption choices of Andrew , taking into
account of how much time and money he can spend each week.
(b) (20%) Suppose Andrew take x hours of piano lessons and goes to y ball games
per week ,then his happiness is x^2y . Find out the per week optimal
consumption of Andrew in his free time and label this consumption in the
diagram of your answer to (a).
(c)(20%) In your answer to (b), is it true that the MRS at the optimal
consumption tangent to some boundary line of all the possible consumption
choices of Andrew? If so, prove it. Otherwise , explain intuitively why the
tangency condition does not have to hold at this optimum,
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