CPI calculation

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

 GDP deflator calculation

Consider an economy with only two goods, X and Y.  

The base year for the GDP deflator in that economy is 1980.

Prices and quantities of the two goods are given in the following table

YEAR               Px        Qx                     Py        Qy                     GDP deflator                 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 GDP deflator values, the inflation rate can only be calculated for certain years (which years and why?)

Computation is easier if we first compute real GDP = value of current quantities at base year prices, and also nominal GDP = value of current quantities at current prices

YEAR  Px        Qx        Py        Qy         Real GDP                                   Nominal GDP

1980     20         50         10         50         20(50) + 10(50) = $ 1500                      $ 1500

2000     25         80         30         50         20(80) + 10(50) = $ 2100         25(80) + 30(50) = $ 3500

2001     25         100       35         40         20(100) + 10(40) = $ 2400         25(100) + 35(40) = $ 3900

2002     30         120       40         50         20(120) + 10(50) = $ 2900         30(120) + 40(50) = $ 5600

Since real GDP = nominal GDP / GDP deflator, we can calculate the GDP deflator as nominal GDP divided by real GDP.

YEAR               GDP deflator                 Inflation rate

1980                  1500/1500 = 1.00           Unknown; no data for 1979

2000                  3500/2100 = 1.67           Unknown; no data for 1999

2001                  3900/2400 = 1.625         - 2.5 percent (a deflation rate of 2.5 percent)

2002                  5600/2900 = 1.931         + 18.83 percent