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UCLA
Economics 11 – Fall 2010
Professor Mazzocco
Problem Set 3
Due by October 14 before 9:00am in the box located outside room 2221E, Bunche Hall
1)
Suppose that an individual with income I cares about two goods, X and Y. The price of
the two goods is P
x
and P
Y
. The individual has the following utility function:
U(X,Y) = X (1 + Y)
a)
Find the Marshallian (uncompensated) demand for X and Y. Are X and Y normal or
inferior goods?
b)
Find the Hicksian (compensated) demand for X and Y.
c)
What is the minimum expenditure necessary to achieve a utility level of U= 72 with
Px=4 and
P
Y
=2?
a)
L(x,y,
λ
) = X(1+Y) +
λ
[I P
x
x – P
z
y]
L
X
= 1 + Y 
λP
x
= 0
(1)
L
Y
= X –
λP
y
= 0
(2)
L
λ
= I P
x
x – P
y
y = 0
(3)
With equations (1) and (2) we get:
P
X
/P
y
= (1+Y)/X
(4)
X
*
=(I+P
Y
)/2 p
x
, Y
*
=(IP
Y
)/ 2p
y
and both are normal goods.
b)
L(x,y,
λ
) = P
x
x + P
y
y +
λ
[U X – XY]
L
X
= Px –
λ(1+Y)
= 0
(1)
L
Y
= Py –
λ(X)
= 0
(2)
L
λ
= U X – XY
= 0
(3)
With equations (1) and (2) we get:
P
X
/P
y
= (1+Y)/X
(4)
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