Prices Indices: Laspeyre, Paasche, and Fisher

7/3/17

A price index is a convenient way to express a change in a diverse group of items. In economics, prices indices are used all the time.

Consider the following table:

	2000	2000	2010	2010
Drink	Unit price	Quantity	Unit Price	Quantity
	po	qo	pn	qn
wine	2.5	25	3	30
beer	4.5	10	6	8
soft drinks	0.60	10	0.84	15

The first price index we'll look at is Laspeyre's. It is a "base weighted" price index. It concentrates on measuring price changes from a base year, and uses quantities purchased in the base year (2000 here) to weight the unit prices in both years. The equation is

L = 100*sum(p_n*q_o)/sum(p_o*q_o)

For this example, L = 126.34.

A drawback of Laspeyre's is that it tends to overweight goods whose prices have increased.

The second price index we'll look at is Paasche's. It is an "end year weighted" price index. It uses the end year (2010 here) quantities as weights. The equation is

P = 100*sum(p_n*q_n)/sum(p_o*q_n)

For this example, P = 125.50.

A drawback of Paasche's is that it tends to overweight goods whose prices have decreased.

Last, there is Fisher's price index. This is the geometric mean of Laspeyre's and Paasche's. The equation is

F = sqrt(LP)

For this example, F = 125.92

The Fisher's price index was developed in an attempt to offset the shortcomings of L and P.

Please check out this spreadsheet so you can play around with the numbers.

There is much, much more to prices indices, but these are the basics. Thanks for reading!