Ch 6 Intertemporal Consumption

However its not that simple from eco 100 recall when

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 inter-temporal 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, inter-temporal UMP. As such, we need to transform the nominal inter-temporal UMP above into a real inter-temporal 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: Inter-temporal Consumption (this version 2012-2013) 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: Inter-temporal Consumption (this version 2012-2013) 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” { inter-temporal budget constraint is: }( ⏟ ( { ) ) ( }( ) ) This budget constraint is in real terms (i.e. in terms of corn) with which the agent’s inter-temporal UMP becomes: ( ) ⏟( ) ( ) ( ) Let’s plot the real inter-temporal budget constraint in a ( we re-write the budget constraint as: ⏟( ) ) plot: on the x-axis we have ( ⏟ and on y-axis we have ) ( ) ( ) 9 ECO 204 Chapter 6: Inter-temporal Consumption (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The x-axis intercept is if the agents spends her entire lifetime income on consumption at maximum amount of...
View Full Document

Ask a homework question - tutors are online