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Unformatted text preview: 22013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. There are many ways to express the “saving at
“graphical” interpretation: Slope of the corners line ” condition and here’s one way interpretation which has a nice Slope of a ray from origin to endowment point This is shown below: * E
( ) Slope Similarly, if she is borrowing at then: This occurs whenever:
[( ) (
[( )
) 24
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Notice that for an agent with complements preferences, regardless of the real interest rate, “once a borrower, always a
borrower”. As before, there are many ways to express the “borrowing at
” condition and here’s one way
interpretation which has a nice “graphical” interpretation: Slope of the corners line Slope of a ray from origin to endowment point This is shown below: E * ( ) Slope Now, the conditions for saving and borrowing at were: As we discussed above, these conditions tell us that whether an agent with complements preferences saves or borrows
has to do with preferences and income but not the real interest rate (i.e. incentive to save/borrow). If an agent is saving
at
then it must be: 25
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Would the agent switch to borrowing if the real interest rate increased or decreased? No. In fact, if an agent is a saver
she will always be a saver no matter how high or low the real interest rate. However, changes in would have an impact
on the amount saved. Look at: ⏟ ⏞ (
[( )
) {⏞
[( } ) That is, if an agent is saving at
then as increases, she will save less! This is in contrast to the agent with CobbDouglas preferences who saves more as . What’s the reason for this “curious” result? The same reason why a person
with a high income may work less as income rises due to an “income” effect. Will savings fall at an increasing,
decreasing, or constant rate? For this we evaluate:
⏞ {⏞
[( That is, as }
) savings decrease at an increasing rate. Now, if an agent with complements preferences is saving at
then we have seen that as
she will save less at
. If you save less today, then when you get old, what happens to your retirement savings account? Will it be
smaller? It turns out that even though you are saving a smaller principal amount, the higher real interest rate “amplifies”
your savings so that your retirement pot is bigger! This is easy to see in this picture: even though you save less at
you have a larger retirement fund at
: 26
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1
0 ( ) ( ) E Notice how the gap between and is larger even though...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto Toronto.
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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