Economics Online Tutor
 Calculating Price Indexes and Inflation: Formulas And Examples
You should be familiar with the information in the main page on inflation

To compute a number for a price index, a base year is used as a starting point.
For the base year price index, the calculation is as follows:

The value of each good in the bundle is computed by multiplying its price
(base year) by its quantity sold (base year).  Then, all of these values in the
bundle are added together.  The result is then assigned a value of 100 for
easy comparison to other years.

The price indexes for years other than the base year can then be compared
with 100 to determine the level of inflation between the two years.

To obtain the price index for years other than the base year: Use the same
bundle of goods that was used for the base year, along with the same
quantities used for the base year, and use the current prices rather than the
base year prices to calculate the value.

Once you have the total value using this method, you compare the total value
for the current year to the base year by dividing the total value (current year)
by the total value (base year), and multiplying the result by 100.  This is shown
mathematically as:

PRICE INDEX (YEAR X) = 100 x (SUM OF (YEAR X PRICE x BASE YEAR
QUANTITY) DIVIDED BY SUM OF (BASE YEAR PRICE x BASE YEAR
QUANTITY))

To calculate the inflation rate between two years, a number of formulas can be
used, depending on which information you are given and which formula you
are comfortable with.  These three formulas are equivalent:
First, if one of the years is the base year, or any year where the price index is equal to 100, then the
calculation for the inflation rate can be simplified to:

INFLATION RATE (BASE YEAR TO YEAR X) = PRICE INDEX (YEAR X) MINUS 100

Second, this simplified method does not work for two years when neither year has a price index equal to
100.  For example, if the price index for year X is 104, and the price index for year Y is 108, you can't
simply subtract and say that the rate of inflation is 4%.  These numbers are based on percentages of the
base year, not percentages of each other.  In this particular example, the inflation rate from a price index
of 104 to a price index of 108, using the second formula above, is:

100 x ((108 - 104) DIVIDED BY 104), OR 100 X (4 DIVIDED BY 104), OR ABOUT 3.845%.
READY FOR AN EXAMPLE TO ILLUSTRATE THE ENTIRE CALCULATION PROCESS?

CONSIDER A HYPOTHETICAL ECONOMY IN WHICH THE BUNDLE OF GOODS USED FOR THE CALCULATIONS
CONSISTS OF ONLY THREE GOODS: GOOD A, GOOD B, AND GOOD C.

THE PRICE AND QUANTITY DATA FOR EACH GOOD AND EACH YEAR (BASE YEAR, YEAR X, AND YEAR Y) ARE
SUMMARIZED IN THE FOLLOWING TABLE:

BASE YEAR      BASE YEAR         YEAR X              YEAR X             YEAR Y            YEAR Y
PRICE           QUANTITY            PRICE             QUANTITY             PRICE           QUANTITY

GOOD A

GOOD B

GOOD C
 \$10 1000 \$10 900 \$12 1100 \$50 1000 \$75 1500 \$80 1250 \$100 10 \$110 10 \$110 15
THE VALUE OF EACH YEAR'S BUNDLE IS SIMPLY THE SUM OF EACH YEAR'S PRICE TIMES QUANTITY FOR
THE THREE GOODS.  THIS WOULD NOT GIVE YOU THE INFORMATION YOU NEED TO DETERMINE HOW
MUCH OF A CHANGE IN VALUE CAN BE ATTRIBUTED TO A CHANGE IN THE OVERALL PRICE LEVEL
(INFLATION), AND HOW MUCH CAN BE ATTRIBUTED TO A CHANGE IN QUANTITY SOLD, OR OUTPUT.  THE
VALUE CALCULATED THIS WAY WOULD BE THE NOMINAL VALUE.  FOR EACH OF THE THREE YEARS, THE
NOMINAL VALUE IS:

BASE YEAR: (\$10 x 1000) + (\$50 x 1000) + \$100 x 10) = \$61,000

YEAR X: (\$10 x 900) + (\$75 x 1500) + (\$110 x 10) = \$122,600

YEAR Y: (12 x 1100) + (80 x 1250) + (\$110 x 15) = \$114,850

THESE ARE ONLY NOMINAL VALUES.  TO DETERMINE THE PRICE INDEX FOR EACH YEAR, FIRST YOU NEED
TO USE THE VALUES BASED ON EACH YEAR'S PRICES TIMES THE BASE YEAR'S QUANTITIES.  THESE WOULD
BE:

BASE YEAR: (\$10 x 1000) + (50 x 1000) + (\$100 x 10) = \$61,000

YEAR X: (\$10 x 1000) + (\$75 x 1000) + (\$110 x 10) = \$86,100

YEAR Y; (\$12 x 1000) + (\$80 x 1000) + (\$110 x 10) = \$93,100

SINCE YOU WANT THE PRICE INDEX FOR THE BASE YEAR TO BE EQUAL TO 100, ASSIGN THE NUMBER 100
FOR THE PRICE INDEX FOR \$61,000.  NOTICE THAT FOR THE BASE YEAR, AND ONLY FOR THE BASE YEAR,
THE NOMINAL VALUE IS EQUAL TO THE TOTAL VALUE USED IN THE PRICE INDEX CALCULATIONS.
FROM THESE TOTAL VALUES, YOU CAN USE THE FORMULA LISTED ABOVE TO CALCULATE THE PRICE
INDEX FOR THE THREE YEARS.  FOR THE BASE YEAR, WE HAVE ALREADY DETERMINED THAT THE PRICE
INDEX IS 100.  FOR THE OTHER TWO YEARS, THE PRICE INDEX WOULD BE CALCULATED AS FOLLOWS:

YEAR X: 100 x (\$86,100 DIVIDED BY \$61,000) = 141 (FOR THIS EXAMPLE, GO AHEAD AND ROUND TO THE
NEAREST 1 POINT.  FOR ECONOMICS CLASS, YOUR INSTRUCTOR SHOULD LET YOU KNOW HOW THE
NUMBERS SHOULD BE ROUNDED)

YEAR Y: 100 x (93,100 DIVIDED BY \$61,000) = 153
NOW THAT YOU HAVE CALCULATED THE PRICE INDEXES FOR EACH YEAR, YOU CAN USE THOSE INDEXES
TO DETERMINE THE RATE OF INFLATION BETWEEN ANY TWO YEARS.  REMEMBER FROM THE ABOVE
DISCUSSION, THE INFLATION RATE FROM THE BASE YEAR TO ANY GIVEN YEAR IS EQUAL TO THE PRICE
INDEX FOR THE GIVEN YEAR MINUS 100.

SO FOR THIS EXAMPLE, THE RATE OF INFLATION FROM BASE YEAR TO YEAR X IS 41%, AND THE RATE OF
INFLATION FROM BASE YEAR TO YEAR Y IS 53%.

TO CALCULATE THE RATE OF INFLATION FROM YEAR X TO YEAR Y:

100 x ((153 - 141) DIVIDED BY 141) =8.5% (ROUNDED)

INFLATION RATE (YEAR X TO YEAR Y) = (100 x (PRICE INDEX YEAR Y
DIVIDED BY PRICE INDEX YEAR X)) MINUS 100

PERHAPS THIS ONE WILL SEEM SIMPLER TO USE:

INFLATION RATE (YEAR X TO YEAR Y) = 100 x ((PRICE INDEX YEAR Y
MINUS PRICE INDEX YEAR X) DIVIDED BY PRICE INDEX YEAR X)

OR:

INFLATION RATE (YEAR X TO YEAR Y) = (TOTAL BUNDLE VALUE YEAR
Y DIVIDED BY TOTAL BUNDLE VALUE YEAR X) MINUS ONE

A couple of things to note about the inflation rate calculations:
 Inflation main page, with links to other pages on the subject of inflation.