The 1995/1996 Household Income, Expenditure - (PDF, 101 mb ...

To fix things mathematically and for intuition's sake, an example will help,
using the following basic data:
V.19
Good 1 Good 2 Expenditure
Period Price Quantity Weight Price Quantity Weight
PI X, 0, P? X? o? M
0 15 5 0.75 2.5 10 0.25 100
t 30 2.5 0.75 2.5 10 0.25 100
Note that PI,O = 15; 0u = .25; etc.,
M O = P ltO Xu + P u Xu = 100, and
PI,O XltO/M O = .75
Using the data above, eq. (21) is
The common Laspeyres Index is
(22)
I = (30),75 (2.5),25= 1.6818
col,O,t 15 2.5
P1,t P 2,t
P1,o X1,o (1') + P2,o X2,o (1')
= 1,'-0 ----'2,0_
(23)
P1,0 X1,0 + P2,0 X2,o
Either eq. (22) or eq. (23) can be used to calculate the Laspeyres Index. Eq.
(23) is a weighted arithmetic mean of the price relatives. Using eq. (22), we
have
Using eq. (23),