Unformatted text preview: lse equal, a small
increase in Graph vs. and vs. .
(6.7) Some finance courses setup and solve for
as in question (6.6) if you solve the UMP: and not and . Show that you get the same expressions for 3
ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (6.8) Consider a 3 period economy (
) with a single good (say, corn). Each consumer receives (individualspecific) real income
(in units of corn) at the beginning of
respectively. The price level at
is
(i.e.
is the base period) and the price levels at
and
are and , respectively.
In each period, the consumer can “borrow” or “save” corn at nominal interest rate
. In this model, “saving” in a
period means that the agent is consuming less than or equal to her income in that period (i.e.
) while “borrowing”
in a period means that the agent is consuming more than her income in that period (i.e.
).
The of total lifetime income is (“future period” is ): (
The of total lifetime income is (“present period” is ) ( ) ):
( ) Suppose a consumer has the following utility function over consumption at
(
Assume all pecuniary variables and : ) . (a) Solve the consumer’s intertemporal UMP for (i)
the parameters. What happens if
?
(b) What happens to the optimal and , (ii) the of , and (iii) the due to, all else equal, a small increase in a small increase in of in terms of
and ? (c) Derive the conditions under which an agent will save in
increase in ? . What happens to due to, all else equal, a small (d) Derive the conditions under which an agent will save in
increase in . What happens to due to, all else equal, a small (6.9) 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. The price level at
is
(i.e.
is the base period)
and the price level at
is . In each period, the consumer can “borrow” or “save” corn at nominal interest rate
. In this model, “saving” in a period means that the agent is consuming less than or equal to her income in that
period (i.e.
) while “borrowing” in a period means that the agent is consuming more than her income in that
period (i.e.
).
The of total lifetime income is:
( The ) of total lifetime income is:
4 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Suppose a consumer has the following utility function over consumption at
(
Assume all pecuniary variables and ( and the , and the of due to, all else equal, a small increase in in terms of the parameters.
and ? (and therefore “borrow” at (d) Derive the conditions under which an agent will “save” in
condition, will the agent continue to “save” at
as ?
and ) of (c) Derive the conditi...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Inflation, S. Ajaz Hussain, Sayed Ajaz Hussain

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