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 chicken-wings is U(X
C
, X
W
)= 2X
C
+ X
W
, where X
C
and X
W
are
chickens and chicken-wings, 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 utility-maximizing bundle (at existing