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Unformatted text preview: ontinue to be a borrower? Show all calculations. . If inflation rises, will she borrow more or less? (d) If the nominal interest rate equals inflation, when will this consumer exhibit consumption smoothing? Show all
calculations.
(6.5) Consider a 3 period economy (
) where at the beginning of
each consumer receives (individualspecific) real incomes
(in units of corn) respectively. In the first two periods, consumers can “borrow” or
“save” corn at the prevailing real interest rate.
Suppose a consumer has the following utility function over consumption at Assume and that the nominal interest rate and inflation rate are and : . (a) Assume a uniform rate of inflation and nominal interest rate between periods
consumer’s intertemporal UMP for
. Show all calculations.
Hints: ● For
we must have
⏟ and . Solve the 2
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. (b) Under what conditions will the consumer save corn at
interest increases? Show all calculations. ? What will happen to savings at (c) Under what conditions will the consumer borrow corn at
interest increases? Show all calculations. if the real ? What will happen to borrowings at if the real (6.6) 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 while “borrowing” in a period means that the agent is consuming more than her income in that period.
The of total lifetime income is:
( The ) of total lifetime income is: Suppose a consumer has the following utility function over consumption at and : (a) Describe the agent’s preferences over consumption “today” versus “tomorrow”. Graph the
constraint (in “real” terms) on a
plot and interpret the and axis intercepts and slope.
(b) Solve the consumer’s intertemporal UMP for
the
of
, and the
parameters. What happens if
? If it’s easier, feel free to make up values for intertemporal budget of
in terms of the
(for example:
or ).
(c) What happens to and the optimal due to, all else equal, a small increase in and ? (d) Derive the conditions under which an agent will “save” in
(and therefore “borrow” at
). According to this
condition, will the agent continue to save at
as ? What happens to and due to, all else equal, a small
increase in ? Graph vs. and vs. .
(e) Derive the conditions under which an agent will “save” in
(and therefore “borrow” at
). According to this
condition, will the agent continue to save at
as ? What happens to and due to, all e...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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