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Unformatted text preview: interest rate is therefore 10%:
Scenario # 2: Inflation rate of 5% Suppose you borrow $100
In real terms, you’ve borrowed 100 units (
)
(
)
Pay back
In real terms, you’re paying back 104.76 units Suppose at
you borrow $100. Since the nominal interest rate is 10%, in
you will pay back $110. Now look at
this problem in real terms (in terms of corn). Observe there is 5% inflation here (
). When you took out
a loan of $100, you really borrowed 100 units of corn. When you pay back the loan, you do so in dollars ($110). In terms
of corn however you’re paying back $110/$1.05 = 104.762 or almost 105 units of corn. That is, you borrowed 100 units
of corn and are paying back (approximately) 105 units of corn: the “real” interest rate is therefore (approximately)
4.76% (observe how the Fisher approximation gives the same answer).
This example demonstrates what you saw in ECO 100 macro: in an inflationary economy, borrowers “win” (and lenders
“lose”) because in real terms borrowers pay back less than what they borrowed. Similarly, in a deflationary economy,
borrowers “lose” (and lenders “win”) because in real terms borrowers pay back more than what they borrowed.
Next, we assume that at
the price of a unit of corn is
and that at
the price of a unit of corn is
allow for inflation/deflation between
and
and denote the rate of inflation by where: . We Notice that:
(
3. Intertemporal UMP Model
Consider an agent who lives for two periods ) in an economy with one good (corn). At the beginning of , the
5 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 is endowed with corn income (the dollar value of which is
) and at the beginning of
, the
(
) ). At
agent is endowed with corn income (the dollar value of which is
the agent can
save/borrow corn at a nominal interest rate of
. She has preferences over consumption at
and
represented by a utility function (
).
We model this agent’s choice of consumption by the intertemporal UMP model:
( ) ⏟
( ) Unlike the consumer theory UMP, in the intertemporal UMP total (lifetime) expenditure always equal total (lifetime)
income. Recalling the time value of money from Math 133 we see that the intertemporal budget constraint can be
expressed:
⏟ ● First, let’s examine the Present Value ( { } ⏟ ) Intertemporal Nominal Budget Constraint: { } ( { } }} } ( ) {{ {{ }} ) This is a nominal budget constraint (in terms of dollars).
Next, we examine the Future Value ( { } ) Intertemporal Nominal Budget Constraint: { } ( ) { ( ) This too is a nominal budget constraint (in terms of dollars).
One can work with either the
or
intertemporal budget constraint and in ECO 204 we will work with
constraint. As such, the agent’s choice of consumption is modeled by the intertemporal UMP model:
( ) budget ⏟
( )
6 ECO 204 Chapter 6: Intertemporal Consumption (this version 20122013) University o...
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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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