### Exploring a Fisher Index

7.
 WHICH MARKETmBASKET? PERIOD 1 PERIOD 2 Items AMOUNT YEAR 1 PRICE YEAR 1 AMOUNT YEAR 2 PRICE YEAR 2 Apples 10 \$.20 8 \$.25 Oranges 9 \$.25 11 \$.21

In the example in the text, we found that using period 1 quantities, the price index in period 2 was

(\$4.39/\$4.25) x 100 = 103.29

Using period 2 quantities, the price index in period 2 was

(\$4.31/\$4.35) = 99.08

You might wonder if it might not be possible to take an average. The great American economist Irving Fisher thought so and proposed that a better price index could be found by taking the geometric mean of the two. To find the geometric mean, multiply the two together and then take the square root.

 What do you get? You need a calculator. If you do not have one, you might be able to use the search line at google.com as one. The google search line at the bottom of this page will not work for this--you have to go to the google home page.

The result is called a Fisher Index, and this procedure is now used in constructing index numbers for U.S. GDP. Whenever you see the U.S. Commerce Department talking about a chain-type index, this is the sort of index they are talking about. The other two indexes also have names. The first one with the early weights is a Laspeyres Index and the second one with late weights is a Paasche index.