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S1 <0 Y 1
1 B A E C’0 C0 Y0
S0 >0 PVY PVY’ C0 S’0 >0
Note: when the intertemporal budget line swivels clockwise around the endowment p oint because the xaxis intercept
becomes smaller while the yaxis intercept Graph ( ) becomes larger. vs. :
33 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. We have
( ⏟ ) (
as long as
Since .
this will always be the case. This is true because
In fact, as condition is given. ∞ then:
[ And as ) then:
[ This means that there must be some where the curve intersects with the [ axis. The can be computed by setting 34
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. ( ) Therefore, the graph looks as follows: S0
Save in T = 0
Borrow in T = 1 1 0 r r* Borrow in T = 0
Save in T = 1 Now let’s see what happens to as increases [( So ) falls as increases. Graphing vs. 35
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. ( [
[ 1 ( ) ) [ 0 r (e) Derive the conditions under which an agent will “save” in
(and therefore “borrow” at
). According to this
condition, will the agent continue to save at
as ? What happens to and due to, all else equal, a small
increase in Graph vs. and vs. .
Answer:
To be a saver in T=1 [ ( ( ( ) ) ) [ 36
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. ( ) [ ( ) ( ) Opposite condition to what we got in d.
    FVY PVY The condition for the agent to be a saver at T=1:
( ) If increases then LHS increases. Therefore if increases sufficiently, then the inequality may reverse and the agent may
become a borrower at T=1.
The other parts of this question are identical to part d. You need to recognize that or or the graph of vs / vs do not change. What changes is the starting point at the graph.
(6.7) Some finance courses setup and solve for
as in question (6.6) if you solve the UMP: and not and . Show that you get the same expressions for 37
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. Answer:
The intertemporal UMP was to choose consumption in each period subject to the constraint that
equals
income:
( ) ( consumption ) To solve the UMP in terms of savings we substitute: Into the UMP budget constraint above to get:
(
(
( )(
)( )( ( ) ( ) )( ) )
( ( ) )(...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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