Unformatted text preview: “save” in
condition, will the agent continue to “save” at
as ? (and therefore borrow at ). According to this Answer:
To be a “saver” at , this consumer would have to consume less than her income: [(
[( ) ) [( ) There are many ways to express the borrowing condition. Here is one way, useful for graphing saving/borrowing
diagrams. The agent saves in
when:
[( ) [( ) 50 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. [(
( The agent “saves” in )
) [(
( ) ) when: The agent will “save” in
(the optimal bundle will be to the right of the endowment point) when the corners line is
flatter than the endowment point ray: Agent borrows in t = 0, “saves” in t = 1
C1
FVY
Y0 < Y1
E Y1
S1 < 0 C1 α/β Y0 C0 PVY C0 S0 < 0
Observe how the condition for
is independent of the real interest rate which means that once a borrower at
the agent will always be a borrower regardless of the real interest rate (albeit the level of borrowings will change). (e) What happens to and due to, all else equal, a small increase in ? Graph Answer:
From above, the condition for the agent to save in vs. and vs. . is: Now, as
the inequality is preserved which means that she will continue to save in
? Let’s see: . But will she save more as 51
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. so long as [( ) ) [(
[( ) [( ) [( [(
( ( ) [( then so long as ) [(
Note how as ) (i.e. the agent is saving at [(
Formally: ⏟) [( ): (
⏟ ) ) ) ) ) The derivative is always negative and given that the agent is saving (i.e. ) this means that as then : Agent saving in t = 0, “borrowing” in t = 1
Suppose r ↑
Agent continues to save in t = 0 but S0 ↓
C1 FVY S’1 < 0 S < 0
1 C’1
C1 A B
Y0 > Y1
E Y1
α/ β C0 C’0 Y0
S’0 > 0 PVY C0 S0 > 0
52
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. The graph of and depends on whether the agent is intrinsically a saver or a borrower. She will be a saver at
where savings are: [(
Because if ) the graph has a negative slope since:
(
⏟ [( ) ) Take the 2nd derivative to see if the graph is linear, strictly concave/convex:
(
[( ⏟
Because
As and , the second derivative is always positive so that the graph is strictly convex. 1 then: ) then:
[( And as ) [( As ) then because ) : [( ) Agent will save at t = 0 if α/β > Y1/Y0
S0 Save in t = 0
Borrow in t= 1 1 r 0 By the same token if the agent is a borrower at if where borrowing (negative savings) are:
53 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 20...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Inflation, S. Ajaz Hussain, Sayed Ajaz Hussain

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