Econ 301  Problem Set #2  Due on Friday, Jun 25, 2010
1.
Constrained Consumer Choice
. Steve’s utility function is
U
=
BC
, where
B
= veggie burgers per
week, and
C
= packs of cigarettes per week. Here
MU
B
=
C
and
MU
C
=
B
.
(a) What is his marginal rate of substitution if veggie burgers on the vertical axis and cigarettes are
on the horizontal axis?
(b) Steve’s income is $120, the price of a veggie burger is $2, and that of a pack of cigarettes is
$1. How many burgers and how many packs of cigarettes does Steve consumer to maximize his
utility?
(c) When a new tax raises the price of a burger to $3, what is his new optimal bundle? Illustrate
your answer in a graph.
2.
Constrained Consumer Choice
. A consumer has the following utility function for goods X and Y:
U
(
X, Y
) = 5
XY
3
+ 10
The consumer faces prices of goods X and Y given by
p
x
and
p
y
and has an income given by
I
.
a. Write out the Lagrangian expression for the consumer’s utility maximization problem.
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 Summer '07
 CORINNELANGINIER
 Microeconomics, Utility, Constrained Consumer Choice, ﬁrst order conditions, Steve consumer

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