© Sanjay K. Chugh
53
Spring 2008
Chapter 4
Inflation and Interest Rates in the
ConsumptionSavings Model
The lifetime budget constraint (LBC) from the twoperiod consumptionsavings model is
a useful vehicle for introducing and analyzing the important macroeconomic relationship
between inflation, nominal interest rates, and real interest rates.
Before doing so, we
present definitions of these terms and a basic relationship among them.
The Fisher Equation
Inflation is a general rise in an economy’s price level over time.
Formally, an economy’s
rate of inflation is defined as the percentage increase in the price level from one period of
time to another period of time.
In any period
t
, the inflation rate relative to period
1
t
−
is defined as
1
1
,
tt
t
t
PP
P
π
−
−
−
=
where
denotes the inflation rate.
30
As a matter of terminology, a
deflation
(negative
inflation) occurs when
π
< 0, and a
disinflation
occurs when
π
decreases over time (but
is still positive at every point in time).
For example, if in four consecutive years,
inflation was 20%, 15%, 10%, and 5%, we say that disinflation is occurring – even
though the price level increased in each of the four years.
In our consideration of the consumptionsavings model, we defined the nominal interest
rate as the return on each dollar kept in a bank account from one period to the next.
For
example, if your savings account (in which you keep dollars) pays you $3 per year for
every $100 you have on balance, the nominal interest rate on your savings account is
three percent.
Because of inflation, however, a dollar right now is not the same thing as a dollar one
year from now because a dollar one year from now will buy you less (generally) than a
dollar right now.
That is, the purchasing power of a dollar changes over time due to
inflation.
Because it is goods (i.e., consumption) that individuals ultimately care about
and not the dollars in their pockets or bank accounts, it is extremely useful to define
another kind of interest rate, the
real interest rate.
A real interest rate is a return that
is measured in terms of goods rather than in terms of dollars.
Understanding the
difference between a nominal interest rate and a real interest rate is important.
An
example will help illustrate the issue.
30
Not to be confused with profits, which is what
π
typically represents in microeconomics.
The usage is
almost always clear from the context.
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54
Spring 2008
Example:
Consider an economy in which there is only one good – macroeconomics textbooks, say.
In the year 2000, the price of a textbook is $100.
Wishing to purchase 5 textbooks
(because macroeconomics texts are so much fun to read), but having no money with
which to buy them, you borrow $500 from a bank. The terms of the loan contract are that
you must pay back the principal plus 10% interest in one year – in other words, you must
pay back $550 in one year.
After one year has passed, you repay the bank $550.
If there
has been zero inflation during the intervening one year, then the purchasing power of that
$550 is 5.5 textbooks, because the price of one textbook is still $100.
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 Spring '11
 chugh
 Inflation, Interest Rates, Sanjay K. Chugh

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