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ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. These conditions tell us that saving and borrowing has nothing to do with morality but rather it has to do with
incentives. For example, if an agent is saving at
then it must be: The decision to save depends on preferences (as represented by the utility parameters), endowments and the real
interest rate. To demonstrate the role of preferences, consider what would happen if the real interest rate increased?
As
the right hand side will continue to be greater than the left hand side and the agent continues to save. This is
because if the agent was already saving, then a higher real interest rate boosts her incentive to save so that she
continues to be a saver. But will she save more, less, or the same? For this we need to look at:
⏞
( ) That is, if an agent is saving at
then as increases, she will save more. Will savings rise at an increasing,
decreasing, or constant rate? For this we evaluate:
⏞
(
That is, as ) savings increase at an decreasing rate. What if an agent is saving at
and real interest rate falls? Then as long as the right hand side of the following
expression is greater than the left hand the agent will continue to be a saver albeit she will reduce her savings (why?): As the interest rate further declines, there will come a point when the right hand side of the following expression
becomes less than the left hand and the agent switches from being a saver to being a borrower: This is because the agent has a lower incentive to save and besides the cost of borrowing is so low that it behooves the
agent, even if she is virtuous and pious, to start borrowing.
If an agent is borrowing (negative savings) at then it must be: 19
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. What would happen if the real interest rate increased? As
the right hand side may continue to be less than the left
hand side so that the agent continues to borrow. But will she borrow more, less, or the same? For this we need to look
at:
⏞
( ) That is, if an agent is borrowing (negative savings) at
then as increases, she will borrow less (after all, borrowings
expressed as a negative number is becoming larger, which means the absolute value of borrowings is getting smaller4) .
Will borrowing rise at an increasing, decreasing, or constant rate? For this we evaluate:
⏞
(
That is, as ) borrowings (negative savings) decrease at a decreasing rate. As the interest rate further rises, there will come a point when the right hand side of the following expression becomes
greater than the left hand and the agent switches from being borrower to being a saver: This is because the cost of borrowing has become prohibitively expensive and besides there is a greater incentive to
save.
The following graphs depict the impact of higher real interest rates on an agent who is saving at
and an agent who
is borrowing at
: notice that as
(slightly) the saver continues to be a saver and...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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