Unformatted text preview: ain. Do not distribute. Now if then ( ) so that the consumer will save whenever: ( ) ( What happens to savings as ) ? Now:
( ) (
[ (
(we need to assume
Now if ) (
) ( ) ( ) ) ). Thus, savings increase when the real interest rate rises.
then ( ) so that the consumer will save whenever:
( ) ( What happens to savings as ) ? Now:
(
( (we need to assume ( [ ) )
) ). Thus, savings increase when the real interest rate rises. (c) Under what conditions will the consumer borrow corn at
interest increases? Show all calculations. ? What will happen to borrowings at if the real Answer
The consumer will borrow corn at when: We need to consider the two possibilities. 22
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. Now if then ( ) so that the consumer will borrow whenever: (
( What happens to borrowing as ) ? Now:
( ) ( ) ( [ ( ) [ ( )
[ This will be positive whenever ) ) ( ( ) ( ) ) which means that the consumer will borrow less as real interest rates rise (remember that if consumer is borrowing then she has negative savings so that a positive derivative means that the
negative savings becomes a larger number or that she borrows less). The expression will be negative whenever
( ) which means that the consumer will borrow more as real interest rates rise (remember that if consumer is borrowing then she has negative savings so that a negative derivative means that the negative savings becomes a
smaller number or that she borrows more).
Now if then ( ) so that the consumer will borrow whenever: (
( What happens to borrowing as ) ) ? Now:
(
( )
) This means that the consumer will borrow less as real interest rates rise (remember that if consumer is borrowing then
she has negative savings so that a positive derivative means that the negative savings becomes a larger number or that
she borrows less). 23
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. (6.6) 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
con...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Inflation, S. Ajaz Hussain, Sayed Ajaz Hussain

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