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Unformatted text preview: Under what conditions will the consumer save corn at
? Characterize:
● The relationship between
and ● The relationship between
Show all calculations. and Answer
To be a saver at , this consumer would have to consume less than her income: [
[ [( [ [( To characterize the relationship between ) [( ) ) [ vs. , we need to first compute
[ [
[ . [( ) [( ) [ [ 8 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, we can find out how and are related:
(
[ Since ( ) ) for the consumer to be a saver at . To characterize the relationship even better, we need to compute the second order derivative:
(
[
Since ( ) ) ( for the consumer to be a saver at Therefore, if the consumer is a saver in ) . This implies a convex relationship. , then as increases, Now, To characterize the relationship between falls and falls at a decreasing rate. vs. , we need to first compute [ [ [( ) [ ( )
[ ( ( ) )(
[ Now, we can find out how [ ( . )[( )( ) ) and are related: 9
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. ( )[( )( )( ( ) )[ ( ( ) ) ) ( ( )] ) )[ (which implies ( ( ) ( (
(
Since ( () ) )
) ) for the consumer to be a saver at . To characterize the relationship even better, we need to compute the second order derivative:
(
[ Since (
relationship. ) ) (which implies ( ) Therefore, if the consumer is a saver in ( ) ) for the consumer to be a saver at , then as increases, . This implies a convex falls and falls at a decreasing rate. (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
literally as perfect substitutes. Under what conditions will
calculations. Assume all pecuniary variables
. as complements, and consumption at
versus
and
? State all assumptions and show all Answer:
Note: This problem is similar to the one in consumer theory where a consumer perceives food and alcohol as
complements, and wine and beer as perfect substitutes for alcohol.
The agent’s problem is:
( ) ( ) ( ) ( ) ( ) For simplicity, write this as:
( ) ( ) ( )
10 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. At the optimum it must be that: We can express the budget constraint in terms of (say)
(
(
( and only: ( ) )
) ( )( ) ( {( ) ( )} {( ) ( )} {(
Note that if then is rising in ) )...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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