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︰經濟系
考試日期（年月日）︰2016/11/07(一)
考試時限（分鐘）：（14:20~17:20）180分鐘
試題 :
1. Melody gets pleasure in gaining knowledge by reading books or in exchanging
gossips (another form of knowledge) by talking to friends. How much knowledge
she gains by reading depends on the quality of book. How many gossips she can
exchange with friends depend on how updated friends are.
(a) (10%)
On Monday she was reading George Stigler's Memoirs. It is a great book. Every
hour of reading brought her 4 units of knowledge. Her friend W was in town
then. Every hour of gossiping with W gave her 2 pieces of gossips. Melody was
busy on Monday. She only had 1 hour to spend on reading and gossiping. Draw
Melody's budget set (in terms of the units of knowledge and the piece of goss-
ips) for the use of her time on Monday. When doing so, label units of knowled-
ge on the X-axis and pieces of gossips on the Y-axis. Write down her budget
line. Denote knowledge by k and gossip by g. Melody spent 7/8 hour in reading,
getting 7/2 units of knowledge and spent 1/8 hour in gossiping, getting 1/4
piece of gossip. (Hint: to get Melody's budget line right, first ask yourself
how much knowledge can she gain if she spent all of her hour in reading? How
many pieces can Melody get if she spent all her hour in gossiping?
(b) (15%)
On Tuesday she was reading The Hitchhiker's Guide to the Galaxy. It is a fun
book but contains less knowledge than George Stigler's Memoirs. Every hour of
reading brought her 2 units of knowledge. Her friend W was still in town. Eve-
ry hour of gossiping with W still gave her 2 pieces of gossips. Melody had mo-
re time on Tuesday. She had 2 hours to spend on reading and gossiping. Melody
spent 3/2 hours in reading, getting 3 units of knowledge and spent 1/2 hour on
gossiping, getting 1 piece of gossip. Applying what you have learned from the
theory of revealed preference, can we infer Tuesday bundle (3 units of knowle-
dge, 1 piece of gossip) is directly revealed preffered to her Monday bundle (
7/2 units of knowledge, 1/4 piece of gossip) ? Does Melody's behavior satisfy
the weak axiom of revealed preference?
(c) (10%)
From Wednesday to Sunday, she read "Three Men in a Boat", her favorite. It is
a humorous account and was initially intended to be a serious travel guide. E-
very hour of reading brought her 3 units of knowledge. Her friend S flew from
Hong Kong to work with her from Wednesday to Sunday. S is serious, every hour
of gossiping with S only gave her 1 piece of gossip. From Wednesday to Sunday
we observed even though Melody might be a busier in one day and less busy in
another day, if she had less than 1/9 hour to spend, she spent all the time on
gossiping. On the other hand, if she had more than 1/9 hour to spend, she spe-
nt exactly 1/9 hour on gossiping and all her remaining time in reading. Could
you make an educated guess on what kind of utility function Melody might have?
2.Consider an economy composed of 16 consumers. Of these, 5 consumers 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{2R,L}, where R and L are,
respectively, the quantities of right and left shoes consumed.
(a) (10%)
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) (10%)
Characterize all Pareto efficient allocations.
3. Consider a very poor consumer who spends his daily income of 200 on bread
(B) which costs 25 per unit and milk (M) which costs 50 per unit. Her prepera-
nce can be described by the utility function
U(B,M)=BM
(a) (10%)
Find this person's optimal daily consumption of bread and milk.
(b) (10%)
Given this consumer's preferences, are bread and milk normal or inferior good?
Explain how you know.
(c) (10%)
Because this consumer is so poor, he must worry about getting the minimum dai-
ly amount of an important nutrient that he needs to stay alive. He gets one
unit of the nutrient per day to stay alive. Draw this consumer's budget set,
taking into account of both this subsistence constraint and his dollar budget
constraint. (Hint: His budget set should now be the part of his dollar budget
set which gives him at least 6 units of nutrient.) Does the consumption bundle
you found in (a) satisfy the consumer's subsistence constraint?
(d) (15%)
Now suppose the price of bread rises to 30 per unit. The price of milk stays
the same. Draw the consumer's new budget set. Find the consumer's new optimal
amounts of bread and milk, taking into account of both his dollar budget cons-
traint and his subsistence constraint.