Taking account of quantities

Some items in the 'basket' are usually more 'important' than others.

    Average retail price of fish ($/kg)
  2005 consumption per capita   2005     2006     2007     2008     2009  
Tarakihi 15.4 kg 19.20 20.78 22.77 25.43 26.67
Gurnard 13.7 kg 18.41 20.15 21.93 24.32 26.42
Snapper  4.6 kg 28.73 30.43 33.67 35.16 37.40

The price of Snapper should have much less influence on the aggregate index than the other types of fish, since much less of it is consumed.

Weighted price index

A weighted price index is more influenced by items with higher consumption and is based on the total amount spent by an average consumer. In 2005, this was:

15.4 × 19.20   +   13.7 × 18.41   +   4.6 × 28.73   =   680.06

Assuming the same consumption for all years,

    $ per capita spent on fish   
  2005     2006     2007     2008     2009  
  680.06     736.05     805.98     886.54     944.71  

The Laspeyres index is a simple price index applied to these totals.

    Laspeyres fish price index   
   2005       2006       2007       2008       2009   
100 108.23 118.52 130.36 138.92

Paasche index

The Laspeyres index uses quantities in the base year as weights. The Paasche index is similar but is based on quantities in the current period.

We only consider the Laspeyres index here.

Formula for Laspeyres index

An equivalent mathematical formula for the index is:

where Q0(j) denotes the quantity of the j-th item in the basket at the base time.