ECON 400
Hartman
Winter 2011
Problem Set IX
(for Wednesday, March 9)
1.
Suppose that an individual's preferences over two goods can be represented by the utility function
(, )
Uxy x
y
.
Let
p
and
s
denote the prices of goods
x
and
y
, respectively, and let
M
denote the individual's
wealth.
a.
What are the Marshallian demand functions and the indirect utility function for this individual?
(Let
1
a
and
1
b
in the solution to problem 1 of Problem Set VIII.)
b.
What are the Hicksian demand functions and the expenditure function for this individual?
(Let
1
a
and
1
b
in the solution to problem 1 of Problem Set VIII.)
c.
Suppose initially that
4
p
,
9
s
, and
216
M
; and that
p
then increases to
9
p
with no change
in
s
or
M
.
i.
How much (total) wealth does the individual need to be as well off after the price increase as
before?
ii.
What is the individual's compensating variation for this price increase?
iii.
What is the maximum amount the individual would pay to avoid the price increase?
iv.
What is the individual's equivalent variation for this price increase?
v.
By how much does the Marshallian consumer surplus change with this price increase?
vi.
Explain the relative magnitudes of the compensating variation, the equivalent variation, and the
change in the Marshallian consumer surplus.
2.
Suppose that an individual's preferences over two goods can be represented by the utility function
(, ) 2
uxy
x y
.
Let
p
and
s
denote the prices of goods
x
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Ellis,G
 Utility, Hicksian demand function, price increase, Marshallian

Click to edit the document details