推 nutta :一隻丁丁八十分XD 11/05 23:12
推 lovehan :水鏡先生表示： 11/05 23:48
課程名稱︰個體經濟學
課程性質︰
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）︰101/11/5
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 :
1. Ding Ding is an optimistic cat, he always looks on the bright side.
His utility function is given below: u(t,s) = max{t,s}
where t stands for how much tuna he gets in a day. Similarly s stands for
how much salmon he gets in a day.
(a) (10 points) Draw some of Ding Ding's indifference curves.
(b) (10 points) Is Ding Ding's preference convex? Explain briefly.
(c) (10 points) Ding Ding is diligent , he spends 24 hours a day to catch
fish. And he is smart, so he is a utility maximizing cat.
On a clear day, catching a tuna costs him 1 hour. It always takes him 2 hours
to catch a salmon no matter what. Calculate his optimal consumption bundle.
In terms of your answer in (b), explain intuitively why his optimal consumption
bundle looks so.
(d) (10 points) On a bad day, it is very hard to get a tuna. Ding Ding has to
spend 4 hours instead to get one tuna. What will Ding Ding consume
on a bad day then ?
(e) (10 points) Decompose the total effect of tuna in (d) to Slutsky's
substitution effect and income effect. Illustrate by a figure.
(f) (10 points) Rephrase Hick's definition as follows. To calculate the
substitution effect, you have to find the smallest budget line so that
Ding Ding still gets the same utility as before. Decompose the total effect
of tuna in (d) to Hick's substitution effect and income effect.
Illustrate by a figure.
(g) (10 points) Compare Slutsky's income effect in (e) with Hick's income
effect in (f). Are they equal ? Explain intuitively your answer.
(h) (10 points) Imagine weather could go from very very fine to very very bad.
Thus on a given day, Ding Ding has to spend p hours to catch a tuna where p is
a positive number. The magnitude of p depends on the weather. Draw Ding Ding's
demand curve of tuna.Plot p on the y axis and his catch of tuna on the x axis.
2.(20 points) 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 a 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)
John in Kaohsiung is another utility maximizer.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 income is 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).
We say that John in Taipei and John in Kaohsiung have the same preference if
their preferences 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, use the idea underlying WARP to make a logical inference on whether
it is possible that John in Taipei and John in Kaohsiung have the same
preferences? If your answer is positive, make an educated guess about what
their preference could be.
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