University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
1
ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 20122013)
Department of Economics (STG), ECO 204, Sayed Ajaz Hussain
_________________________________________________________________________________________________
P
RACTICE
P
ROBLEMS
W
ITH
S
OLUTIONS TO
:
C
HAPTER
3
:
Utility Maximization
Methods in ECO 204
1
Updated: 10/26/2012
(3.1)
Write down
●
the Lagrangian objective function
●
the first order conditions
●
(any) KuhnTucker conditions
●
and
indicate
the possible “signs” of the Lagrange multipliers
(i.e. positive, zero, negative) for the following revenue
maximization problem (do NOT solve the problem):
( )
(3.2)
Write down
●
the Lagrangian objective function
●
the first order conditions
●
(any) KuhnTucker conditions
●
and
indicate
the possible “signs” of the Lagrange multipliers
(i.e. positive, zero, negative) for the following revenue
maximization problem (do NOT solve the problem):
( )
(3.3)
Show if the following utility functions, defined over
{(
) }
, have identical indifference curves:
(a)
(
)
and
? Show all calculations.
(b)
(
)
and
? Show all calculations.
(3.4)
Graph an indifference curve for an arbitrary level of utility
● give
expressions for the indifference curve
equation, intercepts and slope
●
and state (but do not solve) as simplified as possible UMP. Show all calculations.
(a)
.
[
Hint: Do a positive monotonic transformation
]
(b)
(3.5)
A consumer has the following utility function defined over
{(
) }
:
Suppose
and that
and
For feedback, comments and typos please email [email protected]
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
2
ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 20122013)
(a) Without solving the UMP, what i
s impact on the consumer’s utility due to a 1% excise tax on good 1? Show all
calculations.
(b)
Without solving the UMP, what is impact on the consumer’s utility due to a 1% excise tax on good 2?
Show all
calculations.
(3.6)
A consumer’s preferences are
representable by the following utility function over goods 1 and 2 (defined over the
consumption set
{
}
):
√(
)
Does this consumer have rational preferences? Explain.
(3.7)
The following utility functions are given to model
automobile consumers’ preferences over cubic feet of interior
space (good 1) and horsepower (good 2).
Which of the utility is/are
not
suitable?
Give explanations, using graphs if
necessary. In all cases, the utility function is defined over the consumption set
{
}
.
(a)
where
(b)
(
)
where
(
)
is
any
function of
such that
(
)
(c)
where
and
Show all calculations and state all assumptions.
(3.8)
Consider the following utility function defined over the consumption set
{
}
:
(a) Does this consumer have monotone preferences over every bundle in the consumption set? If not, are there
any
bundles in the consumption set where she
does
have monotone preferences? Show all calculations and state all
assumptions.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 AJAZHUSSAIN
 Microeconomics, Utility, Department of Economics, S. Ajaz Hussain, Sayed Ajaz Hussain

Click to edit the document details