Price Indexes and Inflation


It is relatively easy to track the NOMINAL amount spent in two successive years; it would be easy to translate this into a REAL value if there were only ONE GOOD in the economy.

For example, if in 2001 you made $500 in nominal wages per week, and hamburgs cost $4 each, your REAL INCOME would be

$500 / $4 = 125 hamburgs

If in 2002 your nominal wages increase to $600 and the price of hamburgs increases to $6, your REAL INCOME would be:

$600 / $6 = 100 hamburgs

Despite nominal wages having increased, your real wages fall.

However, there's more to life than hamburgs. The price of other goods -- pizza, clothing, health care -- may move very differently than hamburgs.

To keep track of the OVERALL PRICE LEVEL we need to construct a PRICE INDEX to compare prices in any given year to prices in a base year .

In any comparison, you must keep something fixed; in price comparisons, you may choose to fix either the quantities of goods purchased or the prices. Letting both change would only tell you the change in nominal spending; if we fix the consumption basket we have the Consumer Price Index ; if we fix prices we have the GDP deflator .

An example will help:

Suppose that consumers buy two goods, X and Y (durables and non-durables, food and clothing, soda and pizza) In the base year (Year 1) the price of good X is $100 and the price of good Y is $200; in the current year (Year 2), the price of good X is $120 and the price of good Y is $220.

We know that good X has increased 20 percent in price and good Y has increased 10 percent; the overall inflation rate will be someplace between 10 and 20 percent, but where exactly?

Year Px Qx Py Qy
2001 100 50 200 20
2002 120 60 220 40

It is easy to calculate that NOMINAL EXPENDITURE was $9000 in 2001 and $16,000 in 2002

Apply the formula:

Px Qx + Py Qy

In 2001

$100 (50) + $200 (20) = $5000 + $4000

In 2002

$120 (60) + $220 (40) = $ 7200 + $ 8800

But this tells us nothing about how much REAL EXPENDITURE increased.

The Consumer Price Index fixes the consumption basket in the base year, and asks how much it would cost us to buy the same basket in any subsequent year.

In 2002, it would cost

$120 (50) + $ 220 (20) = $6000 + $4400 = $10,400

The CPI for 2002 would be:

Price of Basket in Current Year
-------------------------------
Price of Basket in Base Year

In this case, $10,400 / $9000 = 1.1556

It is conventional to multiply the number by 100, so that the CPI would be reported as 115.56.

The CPI can be read as telling you that:
Prices in the current year are 115.56 percent of prices in the base year.

The CPI inflation rate is the percentage change in the CPI; in our example, it would be 15.56 percent.

The alternative calculation is on the basis of the GDP deflator

The alternative calculation is on the basis of Fix prices in the base year, and compute the price of the actual consumption basket for 2002 at base year prices:

$100 (60) + $ 200 (40) = $ 6000 + 8000 = $14,000

The formula for the GDP deflator in any given year is:

Actual price of this year's consumption basket
----------------------------------------------
This year's basket at base year prices

In the example, the GDP deflator is:

$16,000 / $14,000 = 1.1428.

GDP inflation is 14.28 percent, whereas CPI inflation was 15.56 percent.

Both are perfectly legitimate ways to measure inflation, but they are likely to give different numbers.