CPI calculation -- The Basics
Dr. McGahagan
Consider an economy with only two goods, X and Y.
The base year for the CPI in that economy is 1980.
Prices and quantities of the two goods are given in the following table
YEAR Px Qx Py Qy CPI Inflation rate
1980 $ 20 50 $ 10 50
2000 $ 25 80 $ 30 50
2001 $ 25 100 $ 35 40
2002 $ 30 120 $ 40 50
Note that although you can calculate all CPI values, the inflation rate can only be calculated for certain years
(which years and why?)
Computation is easier if we first compute that price of the base year basket at current prices.
YEAR Px Qx Py Qy Price of base year basket at current prices
1980 20 50 10 50 20(50) + 10(50) = $ 1500
2000 25 80 30 50 25(50) + 30(50) = $ 2750
2001 25 100 35 40 25(50) + 35(50) = $ 3000
2002 30 120 40 50 30(50) + 40(50) = $ 3500
Since the CPI is the price of the base year basket at current prices divided by the price of the base year basket at
base year prices, we divide each number in the final column by $ 1500 to arrive at the CPI.
YEAR CPI Inflation rate
1980 1500/1500 = 1.00 Unknown; no data for 1979
2000 2750/1500 = 1.833 Unknown; no data for 1999
2001 3000/1500 = 2.000 2.00 - 1.833 / 1.833 = 9.11 percent
2002 3500/1500 = 2.333 2.33 - 2.00 / 2.00 = 16.67 percent
