Intermediate Microeconomics
Due: December 31, 2003
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December 24, 2003
Prof. Li-Chen Hsu
Problem Set #4
(10 points) Is the following statement true or false? Briefly explain your answer.
(a) If a utility maximizer is a net seller of something and the price of that good rises
while other prices stay constant, her situation might improve so much that she
becomes a net buyer.
(b) If a person is a net supplier of a normal good, and its price increases while all other
prices stay the same, then his demand for the good must decrease.
(10 points) Andy’s demand function for Coca is xc  0.2m  3Pc . The price of Coca used
to $2, the price of Pepsi used to be $3, and his income used to be $50. If the price of
Coca increased to $3 and the price of Pepsi stayed constant.
(a) How much is the substitution effect of x?
(b) How much is the income effect of x?
3.
(10 points) Charlie’s utility function is ln x  ln y . The price of x used to be $1 per unit
and the price of y was $2 per unit. His income was $50 per day. If the price of x
increased to $2.25 and the price of y fell to $1.25,
(a) What the optimal choice before the change of prices?
(b) In order to be able to just afford his old bundle, how much daily income would
Charlie have to have?
4.
(9 points) Mike insists on consuming 4 times as much of y as he consumes of x(y=4x).
The price of x is 3 times the price of y. Mike has an endowment of 20x’s and 45y’s
which he can trade at the going prices. He has no other source of income.
(a) What is Mike’s gross demand for x?
(b) What is Mike’s net demand for x?
(c) What kind of preferences does Mike has?
5.
(12 points) Shirley consumes two goods, x and y. The price of x is $5 and the price of y
is $5. Her utility function is U ( x, y)  x 2 y .
(a) If Shirley is endowed with 6 units of x and 5 units of y, how many units of good x
and y will she consume?
(b) If the price changes to $9 for x and $9 for y, how many units of good x and y will she
consume?
(c) Does the result of (a) and (b) the same? Why?
6.
(9 points) Jackie’s net demands for x and y are (5, -5) and her gross demands are (12, 15).
What is her initial endowment of x and y?
7.
(20 points) Please draw the (1) Marshallian, (2) Hicksian, and (3) Slutsky demand curve
at the following situations.
(a) x is an Giffen good and the price of x goes down.
(b) x is a Giffen good and the price of x goes up.
(c) x is a normal good and the price of x goes up.
(d) Try to compare the meaning of the three kinds of demand curves.
8.
(10 points) Silly’s utility function is U ( x, y)  xy 3 . She is endowed with 51 units of x and
7 units of y. The price of x is $1 and the price of y is $3.
(a) Find her net demand of x.
(b) Find her net demand of y.
9.
(10 points) Suppose a consumer has preferences between two goods that are perfect
substitutes. Can you change prices in such a way that the entire demand response is due
to the income effect?