**How to calculate the CPI and inflation rate:**

First
we need to know how much of each good were purchased each year and what the
prices were:

Hamburger Jeans Movie
Ticket

1984
Price $.80 $24 $5.00

1984
Quantity 40 1 4

Then
find total expenditure by multiplying price times
quantity and adding them:

Expenditure = (.80 x 40) + (24 x 1) + (4 x 5)
= $75

$32 + $24 + $20 = $75

Now,
20 years later, we have new prices:

2004: Hamburger Jeans
Movie Ticket

$1.20 $30 $7.00

Assume
that the market basket (the amount purchased) stays the same in 2004 as it was
in 1984 and the only thing that’s changed are prices. Now what does that market basket cost in
2004? Use 1984 prices and 2004
quantities.

(The
BLS assumes the same market basket each year)

($1.20
x 40) + ($30 x 1) + ($7 x 4) = $106

$48 + $30 + $28 = $106

To
find the CPI in any year, divide the cost of the market basket in year t by the
cost of the same market basket in the base year.

The
CPI in 1984 = $75/$75
x 100 = 100 The CPI is just an index value and it is
indexed to 100 in the base year, in this case 1984.

To
find the CPI in 2004 take the cost of the market basket in 2004 and compare it
to the same basket in 1984:

CPI
in 2004 = $106/$75 x 100 = 128.0

Now
we can calculate the inflation rate between 1984 and 2004:

(128 – 100) /100 = 28/100 = 28%

So
prices have risen by 28% over that 20 year period. If the period was 1984 to 1985 we would say
that inflation was 28% in 1985.

Now
suppose that we know that the CPI in 1972 was 37.5 (where 1982 = 100) and that
gasoline costs 36 cents per gallon. The
CPI in 2004 is 188.9. The 36 cents is a
nominal figure. In 2004 dollars, what
did gasoline cost in 1972?

Price
in dollars of the original year x (Price level in 2004/Price level in original
year)

36
cents x (188.9/37.5) = .36 x 5.03 = $1.81

So
36 cents in 1972 is the same as $1.81 in 2004 dollars. Gasoline is about $1.95 today so it is only a 14 cents more expensive than it was 34 years
ago.

You
can find a calculator that does this automatically at http://minneapolisfed.org/Research/data/us/calc/index.cfm

---Art
Woolf

February
25, 2005