Computing a Price Index

Let's see how a price index like the Consumer Price Index is computed. The best way to show that is by an example. To keep it (unrealistically) simple, we will look at an example with just two goods: chicken and beans. Here, in Table 1, is the data we will use for the example.

Table 1

	1995			1996
	price	quantity	expenditure	price	quantity	expenditure
chicken	2	5000	10000	2.75	4131	11360.25
beans	0.75	10000	7500	0.8	12987.19	10389.75
total			17500			21750

We see that in this case, both prices have increased, but they have increased at different rates. The price of chicken increased from $2 to $2.75, a 37.5% increase, while the price of beans has increased from .75 to .8, a rate of six and two-thirds percent. How are we to combine these two quite different rates of "inflation?" One possibility: we might use a "Laspeyres Price Index."

The Consumer Price Index is an example of a "Laspeyres Price Index." In turn, a Laspeyres Price index is defined in this way. First, as with any comparison of prices or productivity, we have to define a "base year." In the example, 1995 will be our base year. Then:

Laspeyres Price Index: The Laspeyres Price Index is the cost of buying what people bought in the base year at the prices they pay in the current year, divided by the cost of the same goods and services at the prices actually paid in the base year, times 100.

Here is a summary of the computation for the example, in Table Two. We see that the 1995 quantity of chicken, 5000 chickens, priced at the 1996 prices, would cost 2.75 times 5000 = 13,750 dollars. Similarly, the base year purchase of beans, at 1996 prices, would cost 8000, giving the total cost for the 1995 goods and services at 1996 prices as 21,750. Since 1995 expenditure for those same goods was 17,500, the rate of increase is (21750-17500)/17500 = 4250/17500 = 24%.

Table Two

	1996 prices	1995 Quantities	expenditure
chicken	2.75	5000	13750
beans	0.8	10000	8000
total			21750
1995 spending			17500
Price Index			124
Rate of increase			0.24

In the example, for our simple two-good economy, we have a price index of 124 and a rate of inflation of 24%.

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