课程名称︰个体经济学上
课程性质︰经济系大二必修
课程教师︰黄贞颖
开课学院：社会科学院
开课系所︰经济系
考试日期（年月日）︰2020/11/09
考试时限（分钟）：180
试题 :
There are 10 questions in the exam, and each worth 10 credits.
1. Ding Ding is a cat philosopher. He spends his time on two activities,
sleeping and thinking. Both activities produce pleasure to Ding Ding.
How effective Ding Ding is in each activity varies day by day. But on
a given day, if he spends "s" effective hours in sleeping and "t"
effective hours in thinking, his utility is u(s, t) = s^2 + t. You can
assume that time is continuous in answering the following question.
(a) Let us first ignore that there are only 24 hours each day. Label
"s" on the x-axis and "t" on the y-axis in a diagram. Draw two
indifference curves u(s, t) = s^2 + t = 24^2 = 576 and u(s, t) =
s^2 + t = 12^2 = 144. On each indifference curve, you have to mark
at least the coordinates of four points to illustrate the shape of it.
(b) Describe in words how these two indifference curves in (a) relate to
each other.
(c) On a quiet day, Ding Ding is effective. Every hour he spends on
sleeping is an effective hour. Similarly, every hour he spends on
thinking is an effective hour. So his budget line of the day is
s + t = 24. Illustrate the optimal choice of Ding Ding in a diagram.
What is the optimal effective hour "s"? What is the optimal effective
hour "t"?
(d) On a noisy day, Ding Ding is not so effective in sleeping but just as
effective in thinking. Therefore, every two hours he spends on
sleeping is an effective hour. But every hour he spends on thinking
is an effective hour. So his budget line of the day is 2s + t = 24.
Illustrate the optimal choice of Ding Ding in a diagram. What is the
optimal effective hour "s"? What is the optimal effective hour "t"?
(e) Decompose the change in the optimal effective hour from (c) to (d)
into Slutsky substitution effect and income effect. Illustrate this
in a diagram. Pin down the exact amount of the substitution effect
and that of the income effect.
(f) Suppose the noisiness of a day is captured by a parameter "n" > 0. On
such a day, every "n" hours Ding Ding spends on sleeping is an effective
hour. But every hour he spends on thinking is an effective hour. So
his budget line of the day is ns + t = 24. Find the minimal n such
that Ding Ding spends a positive amount of time on thinking.
(g) Continue from (e), draw Ding Ding's Demand curve of effective hour "s"
on sleeping. On this demand curve, the price is simply "n" and "n" can
vary from high (very noisy) to low (very quiet). The quantity is simply
the optimal effective hour "s" at every corresponding "n". Write down
the price-quantity relation of each part of the demand curve clearly.
(h) Because various online forums to exchange philosophical thought are
readily available. Ding Ding becomes more effective in thinking when
he has access to these forums. Every hour he spends on thinking
becomes f > 1 effective hour. For a fixed level of n, write down Ding
Ding's budget line. Is the following possible? "With this fixed "n",
changing from a day with no access to the forums (f = 1) to another day
with access (f > 1). Because Ding Ding becomes more effective in
thinking, he will spend fewer hours in thinking when he has access.
This will make him spend more hours in sleeping, so we will see "s"
increasing when he has access." Explain your logic in words.
2. Mr. Smith and Mr. Jones both spend their money only on education and foods.
They are both utility maximizers. A basket (x, y) is a consumption bundle
where the amount of education is x and of foods is y. You observe that
when the price of education is 4 and the price of foods is 2, Mr. Smith's
unique optimal consumption basket is (3/2, 1). You also observe that when
the price of education is 2 and the price of foods is 4. Mr. Jones's unique
optimal consumption basket is (1, 3/2)
(a) We say that Mr. Jones cares more about education than Mr. Smith if
whenever Mr. Smith weakly prefers basket A to B, and the amount of
education in A is strictly greater than that in B, then Mr. Jones
strictly prefers basket A to B. Can Mr. Jones care more about
education than Mr. Smith? Explain briefly.
(b) We say that Mr. Smith and Mr. Jones 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.
Is it possible that Mr. Smith and Mr. Jones have the same preference?
Explain breifly.