Percentage Change
Suppose you
have an index with a base year 1990 and the index value is therefore 100. Compare that the year 2000 which has a value
of 164. This means that inflation grew
by how much over the decade?
% change
= [(new year – base year) / base year]
= [(164 – 100) / 100]
= 64 / 100
= 0.64 or 64.0%
This is the
standard method of calculating percentage change.
Year |
Nominal Price |
CPI[1]
|
Real Price |
1980 |
$1.29 |
86.8 |
|
1990 |
$1.79 |
132.4 |
|
2000 |
$2.59 |
167.8 |
|
We want to
compare the prices so to net out general inflation we can adjust the 1980 and
1990 nominal prices into real prices in year 2000 dollars.
We should
first ask: Which CPI measure should we use?
All Items or Food and Beverages make sense. Milk is, after all, a beverage.
How do we do
this calculation? Again, we have to
adjust the nominal price.
Real
Pricez = (Nominal Pricez
) x (Adjustment Factor)
The
adjustment factor is formed using the CPI measures
Real
Pricez = (Nominal Pricez
) x (CPIbase year / CPIz)
Here we use the nominal price
of 1980 milk ($1.29) and adjust them to the 2000 dollars in order to allow me
to directly compare them. Remember the
data we have:
Year |
Nominal Price |
CPI[2]
|
Real Price |
1980 |
$1.29 |
86.7 |
|
1990 |
$1.79 |
132.1 |
|
2000 |
$2.59 |
168.4 |
|
Real
Price of 1980 milk in year 2000 dollars =
(Nominal Price1980 )
x (CPI2000 / CPI1980)
Real
Price of 1980 milk in year 2000 dollars = ($1.29) x
(168.4 / 86.7)
Real
Price of 1980 milk in year 2000 dollars = ($1.29) x
(1.9423)
Real
Price of 1980 milk in year 2000 dollars = $2.51 in year 2000 prices
Now I have
both prices in terms of year 2000 prices and I can compare. What has happened to the real price of milk?
PRACTICE: What is the price of milk in 1990 brought to
year 2000 cost of living?[i]
Another use of a Price Index
Suppose you make $42,000 a
year in Nashville and you are contemplating a move to Atlanta. You investigate
and find that your salary in Atlanta would be $49,000. Are you thrilled?
It depends
on the cost-of-living! Suppose that the
CPI in Nashville is 92.5 and the CPI value for Atlanta is 121.8. What matters is the purchasing power of that
salary and we can get some idea about by looking at a cost of living index in
each of the cities. While this is not a
perfect measure it is far better than nothing!
Real
Salary in ATL refers to how you would view the
salary as a person from Nashville.
You’re essentially putting the Atlanta salary into the Nashville dollars
that you understand. Calculation:
Real
Salary in ATL = (Nominal
SalaryATL ) x (Adjustment
Factor)
Real
Salary in ATL = (Nominal
SalaryATL ) x (CPINVILLE
/ CPIATL)
Real
Salary in ATL = (Nominal
SalaryATL) x (CPINVILLE
/ CPIATL)
Real
Salary in ATL = ($49,000)
x (92.5 / 121.8)
Real
Salaryin ATL = $37,213
Your
current salary in Nashville is $42,000 per year, and while the salary in
Atlanta is higher in nominal terms in terms of its real purchasing power the
amount of goods and services you could buy in Atlanta would be comparable to
what one could buy in Nashville for $37,213.
You are actually $4,787 better off in Nashville! Why?
Because
the cost of living is higher in Atlanta and you have just adjusted to find that
out!
Caveats about Price Indexes:
1)
Quality changes
over time. Between 1980 and now we have
gone through the death of 8-track tapes, cassette tapes, and we are watching
the eclipse of CDs with the advent of MP3 files and players.
2)
The price index
measures very specific things. Be sure
that you are using a price index that captures what you want.
3)
The CPI is often
referred to as “cost-of-living” index which is true only if you buy the same
basket as the one the CPI is constructed with.
Unlikely! But sometimes the next
best solution is all that you have…
[1] The Economic Report of the President 2007, Table B-60. – Consumer price indexes for major expenditure classes, 1960-2007
[2] The Economic Report of the President 2007, Table B-60. – Consumer price indexes for major expenditure classes, 1960-2007