Econ 100A  Problem Set 2
Utility Maximization and Demand
1.
George’s utility is given by U(x
1
, x
2
) = 6x
1
*x
2
2
. Use calculus to work through the
utility maximization problem and derive his demand functions x
1
(p
1
, p
2
, I) and x
2
(p
1
,
p
2
, I).
2.
Ted’s demand function for goods 1 and 2 is given by U(x
1
, x
2
) = 3lnx
1
+ 2x
2
. Derive
his demand function for good 1.
3.
When Lisa cooks a chicken she only eats the chicken wings. Her utility function over
whole chickens and chickenwings is U(X
C
, X
W
)= 2X
C
+ X
W
, where X
C
and X
W
are
chickens and chickenwings, respectively.
What is her demand function X
C
*
(p
c
, p
w
, I)
for chickens?
4.
If x
1
(p
1
, p
2
, I), x
2
(p
1
, p
2
, I) are my demand functions for commodities 1 and 2, and
MRS(x
1
, x
2
) denotes my marginal rate of substitution at the commodity bundle
(x
1
, x
2
), what is the
numerical value
of the expression
MRS(x
1
(1,3,12), x
2
(1,3,12))?
(Assume x
1
and x
2
are positive.)
5.
My utility function is U(x
1,
x
2
) = 2x
1
2
x
2
and my utilitymaximizing bundle (at existing
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 '07
 Babcock
 Economics, Supply And Demand, Utility, demand function, demand functions

Click to edit the document details