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Unformatted text preview: et constraint and noting that the left side equals 11
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. the right side3:
( ) ( ) ( ) ( ) Remember: the real
intertemporal budget constraint always passes through the endowment point. As such, in
contrast to consumer theory, the budget line will not swivel on either intercepts. For example, suppose the real interest
rises (when would this happen?). In that case, the xaxis intercept falls (since as
), the yaxis intercept
increases (since as
), and the budget line slope increases, so that: Suppose ↑ ( E ) ( ) Before we do some UMPs, let’s think about what the position of the optimal choice vis a vis the endowment point –
what would this tell us? Take a look at the graph below which shows the optimal choices and endowment points of
three agents A, B and C: 3 After all, how do you check if a line goes through a point?
12 ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Agent C Agent B Agent A A E E= E
( ( ) C ) ( ) B
45o 45o 45o Notice all three agents’ endowment point is above the 45 degree line: this means that
income at
is greater than their income at
. Notice that: or that all three agents’ Agent A’s optimal choice is above the 45 degree line so that she consumes more at
than at
and that
which means she saves at
allowing her to consume more than her income at
(in fact, notice
that
)
Agent B’s optimal choice is below the 45 degree line so that she consumes more at
than at
and that
which means she borrows at
due to which she consumes less than her income at
(in fact,
notice that
)
Agent C’s optimal choice coincides with the endowment point which means that she neither saves or borrows
at
which means that she must consume all her income at
. This shows that if an agent saves when she’s young she gets to consume more than her income when she’s old; if an
agent borrows when she’s young she must consume less than her income when she’s old; and that if an agent neither
saves or borrows when she’s young then she must consume all her income when she’s old. In particular, agents can’t
save or borrow in both periods.
Based on our discussion, the general intertemporal UMP model is:
( ) ( ) ⏟( ) 13
ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. For convenience, denote the
of the total lifetime real income as
model can be succinctly expressed as:
( ) ( with which the general intertemporal UMP ) We now do specific cases of the intertemporal UMP.
3. CobbDouglas Intertemporal UMP Model
Consider an agent who perceives consumption at
choice must have some corn in both periods (i.e.
utility model: and
as imperfect substitutes and who at the optimal
). We can represent her preferences by the CobbDouglas Where
are utility parameters and the utility functio...
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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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