University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
1
ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption 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
6: Modeling Intertemporal Consumption
1
Updated: 1/21/2013
Fixed typos are in yellow
(6.1)
Consider a 2 period economy (
) with a single good (say, corn). Each consumer receives real income
(in
units of corn) at the beginning of
respectively. Denote the real interest rate by
(assume a common
at
).
Suppose a consumer has the following utility function defined over the consumption set
{(
) }
:
(
)
(
)
Assume all pecuniary variables
.
(a) Derive an expression for
the
of
(Future Value of Total Lifetime Income), and the
of
(Present
Value of Total Lifetime Income). State all assumptions and show all calculations.
(b) Under what conditions will the consumer save corn at
? Characterize:
●
The relationship between
and
●
The relationship between
and
Show all calculations.
(6.2)
Consider a 3 period economy (
) with a single good (say, corn). Each consumer receives real income
(in units of corn) at the beginning of
respectively. Denote the real interest rate by
(assume a
common
at
).
Suppose a consumer has the following utility function defined over the consumption set
{(
) }
:
(
)
(
)
That is, the consumer perceives consumption at
and
as complements, and consumption at
versus
literally as perfect substitutes. Under what conditions will
and
? State all assumptions and show all
calculations. Assume all pecuniary variables
.
(6.3)
In this 1 period problem, a consumer allocates her income
between consumption
and savings
. Her utility
function is:
1
Thanks to Akber Nafeh for preparing these problems and solutions. Also thanks to Samantha Pettinato.
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
2
ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption in ECO 204 (this version 20122013)
( )
Assume
.
(a) Solve the consumer’s UMP. Show all calculations and clearly state any assumptions.
(b) Is it possible that this consumer “goes hungry” (i.e. consume nothing)?
(6.4)
An individual lives for two periods (
and
) in an “e
corn
omy” (i.e. the only good is corn). Her real income
(measured in corn) is
in
and
in time
.
is the base period so that
and allow for the possibility of inflation (i.e. it may be that
). Denote
the nominal interest rate by
, inflation by
and the real interest by
.
Consider a consumer with the following utility function for consumption in
and consumption in
:
(
)
Assume
.
In this question you do not have to derive the intertemporal budget constraint from 1
st
principles (i.e. you can state the
constraint).
(a) Calculate the consumer’s optimal consumption in
. Show all calculations and clearly state any assumptions.
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Inflation, S. Ajaz Hussain, Sayed Ajaz Hussain

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