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Unformatted text preview: f Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) ( ⏟ ) (
( )
) At this point it would appear that are ready to solve this nominal intertemporal UMP. However, it’s not that simple.
From ECO 100 recall when making decisions over time, decisions should make decisions on the basis of real and not
nominal variables which is why you studied real wages, real GDP, real money supply etc. In the same vein, the agent
should choose
on the basis of a real, not nominal, intertemporal UMP. As such, we need to transform the
nominal intertemporal UMP above into a real intertemporal UMP. Start with:
( ⏟ ) (
( ) (
⏞ { ⏟
( }( ) ) ( ) { ) }( ) ) { }( ) This expression is in real terms because nothing here is in terms of money. We now argue that the expression ( ) can be interpreted and defined as:
( ) Here’s why. Look at:
{
Suppose }( ) which means the agent saved all or part of her income at
. With this interpretation the expression above becomes: . Then we can say: savings today { }( ) But surely, what you consume tomorrow is equal to: Because this expression is in real terms we can define:
{ }( )
7 ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. This yields:
{ }( ) Comparing this expression with:
{ }( ) Implies that:
( ) We denote the real interest rate by so that:
( ) This is the only exact definition of the real interest rate and in stark contrast to some texts and courses which
erroneously state that
In fact, if the rate of inflation is small, only then can we state this approximation: But why bother with this approximation when you can use the exact result
assume the agents borrowed at
. Suppose
“borrowings” (actually negative savings) today is . The result arises even if we which means the agent borrowed at
. Then we can say:
With this interpretation the expression above becomes:
{ }( ) Again, what you consume tomorrow is equal to: Because this expression is in real terms we can define:
{ }(
{ )
}( ) Comparing this expression with:
8
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. { }( ) Once again we can define the real interest as:
( ) With this definition of the real interest rate, the “real”
{ intertemporal budget constraint is: }(
⏟
( { ) ) ( }( ) ) This budget constraint is in real terms (i.e. in terms of corn) with which the agent’s intertemporal UMP becomes:
( ) ⏟( ) ( ) ( ) Let’s plot the
real intertemporal budget constraint in a (
we rewrite the budget constraint as:
⏟( ) ) plot: on the xaxis we have (
⏟ and on yaxis we have ) ( ) ( ) 9
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The xaxis intercept is if the agents spends her entire lifetime income on consumption at maximum amount of...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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