课程名称︰个体经济学一
课程性质︰大学部大二必修
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）︰2015.11.9
考试时限（分钟）：180分钟
试题 :
1.Rachel only consumes two goods: books (b) and video games (v). Her prefe-
rence is lexicographic. That is, for any two consumption bundles of books and
video games (b1,v1), (b2,v2), she weakly prefers (b1,v1) to (b2,v2) if either
b1>b2 or b1=b2 but v1>=v2 (where b1 is the number of books in the first bun-
dle (b1,v1), v1 is the number of video games in the first bundle (bi,v1), b2
is the number of books in the second bundle (b2,v2), v2 is the number of video
games in the second bundle (b2,v2)). In all your diagrams, label books on the
x axis and label video games on the y axis.
(a)(10pts)
Draw Rachel's indifference curve.
(b)(10pts)
Show that Rachel's preference is homothetic.
(c)(10pts)
Suppose the price of books is 1 and that of video games is also 1. Derive Ra-
chel's income offer curve and Engel curve of video games.
(d)(10pts)
Suppose Rachel's income is 100 and the price of video games is 1. Derive Rach-
el's demand curve of books.
2.You are given the following partial information about a consumer's purchases
. He consumes only two goods:
Year 1 Year 2
Quantity Price Quantity Price
Good 1 100 1 Good 1 120 1
Good 2 100 1 Good 2 ? 0.8
Over what range of quantities of good 2 consumed in year 2 would you conclud:
(a)(10pts)
That the consumer's consumption bundle in year 1 is directly revealed preferr-
ed to that in year 2?
(b)(10pts)
That the consumer's consumption bundle in year 2 is directly revealed preferr-
ed to that in year 1?
(c)(10pts)
That his behavier satisfies the weak axiom of revealed preference?
(d)(10pts)
You are additionally told that in year 3, when the price of good 1 is 0.8 and
that of good 2 is 1, the consumer consumes 125 units of good 1 and 100 units
of good 2. Over what range of quatities of good 2 consumed in year 2 would you
conclude that his behavier satisfies the strong axiom of revealed preference?
3.Consider an economy composed of 16 consumers. Of these, 5 comsumers each own
one right shoe and 11 consumers each own one left shoe. Shoes are indivisible.
Everyone has the same utility function, which is Min{R,L/2}, where R and L are
, respectively, the quatities of right and left shoes consumed.
(a)(10pts)
Is the status quo (where each individual has his own shoe) Pareto efficient?
If so, briefly explain why. If not, provide a Pareto improvement.
(b)(10pts)
Characterize all Pareto efficient allocation.