Laspeyres index and Paasche index

Laspeyres Index is “fixed-weighted” or “Same-weight” index or Prices are weighted by quantities in Base period. This means we always take the quantities, that we used in base period. Refer this article for example .

Whereas in Paasche index, prices are weighted by the quantities of the current period. That is every time index is made (other than base year), Quantities are going to be different.

Laspeyres formula :

Laspeyres index

Pc is Price of commodity
qc is quantity of commodity
tn is reference period of current year
t0 is reference period of base year

Let’s take an example:
2010(Base year):
Price of donut is 10 rs. Quantity is 5
Coffee price = 5 rs. Quantity is 2.

Base year index PL (2010) = (10*5)+(5*2) / (10*5)+(5*2) = 60/60 = 1

In 2015(Current period):
Price of donut is 20 & quantity is 8
Price of coffee is 10 & quantity is 19

Current year PL (2015) = { [20(2015)*5(2010)] + [10(2015)*2(2010)] } / { [10(2010)*5(2010)] + [5(2010)*2(2010)] } = 120/60 = 2.

Paasche index:

Paasche index

Pc is Price of commodity
qc is quantity of commodity
tn is reference period of current year

Pp (2010) = (10*5)+(5*2) / (10*5)+(5*2) = 60/60 = 1

Pp (2015) = { [20(2015)*8(2015)] + [10(2015)*19(2015)] } / { [10(2010)*8(2015)] + [5(2010)*19(2015)] } = 350/175 = 2

In plain terms, Paasche focus on Base year, How much income of base year has to be reduced, so that individual may buy same products, as she can buy in current period. (Imagine after inflation, in current period she will purchase less compared to base year)

Laspeyres is focusing on Current period, as quantity remain same, only price changes. How much income of current period has to be increased, so that same quantity of products can be purchased.

Got Something To Say:

Your email address will not be published. Required fields are marked *

*
*