Unformatted text preview: tertemporal Consumption in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. This takes the same form as in consumer theory where where now, instead of income we use income: Which is the MU of FVY. To compute the MU of PVY, restate Lagrangian in terms of PVY. [(
( ) ) ( )] ( ) Which is the MU of PVY.
If : ( (c) What happens to and the optimal ) due to, all else equal, a small increase in and ? Answer:
(i) [ ( )( )( )] ) ( ( ( [ ) ) (ii)
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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. ( ) ( ) [ ( ) ) ) [( ( (iii) [ If the agent is a borrower today then ( )] ( [ ( ) , if the agent is a saver today then ) ( ) ⁄ From part b: (d) 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 at , this consumer would have to consume less than her income: 30
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. [ There are many ways to express the borrowing condition. Here, we do it in terms of the
relative to the slope of the budget line:
[ [ Crossmultiply by ( ) and the inequality will have the same sign as long as (
( ( or : budget line: )
(
⏟
 ) ) ) The left hand side of this equation is the absolute value slope of the The right hand side of the equation ( at the endowment point is the  )
  of the indifference curve at the endowment point since: 31
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. At the endowment point ( ) ( ) so that:
  Therefore, the agent will save in
when the optimal choice is to the left of the endowment point, which happens
when the budget line is steeper than the slope of the indifference at the endowment point:
( ) If you want to show someone with CobbDouglas preferences saving when they’re young, make sure you draw the graph
with budget line flatter than the indifference curve slope at the endowment point: C1 Save when young
(α/β)(Y1/Y0) ≤ (1 +r) FVY C1
S1 < 0 E Y1 C0 Y0 PVY C0 S0 > 0 From above, the condition for the agent to save in is:
( ) Or: Now, as the right hand side of this inequality becomes larger so that the inequality is preserved which means that she will continue to save in .
32 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. But will she save more as ? Let’s see: so long as [
Now, the impact on savings when is (remember that the derivate ⏟ ( is for the case where : ) The derivative is always positive. Given that the agent is saving (i.e. ) this means that as then . Agent saving in t = 0, “borrowing” in t = 1
Suppose r ↑
C1
Agent continues to save
FVY’
C’1
FVY
S’1 <0...
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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.
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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