Laspeyre’s Weighted Aggregative Method

The method devised by the German Economist Etienne Laspeyre in 1871 for calculating the price indices for a current period is known as Laspeyre’s method of index number. Under this method, we get the weighted index on the basis of aggregative expenditure assuming that the quantities consumed in the base year are also the quantities consumed in the current year. As such, the index number is calculated by the following formula:

P₀₁(L) =  (∑ p1q0/∑ p0q0) x 100

Where, P₀₁(L) = Laspeyre’s Index of the current year on the basis of the base year.

i.e. aggregate of expenditure in the current year.

∑ p1q0 = Sum of the products of the price of the base year, and quantity of the base year.

i.e. aggregate of expenditure made in the base year.

Merits

The chief merits of this method are as follows:

• It is very to understand, and simple to calculate.
• It is based on fixed weights as the quantity of the base year are taken as weights of the items in both the years.
• It is not necessary to determine the weights on any other basis every time an index number is constructed.
• It satisfies the unit test of adequacy which means that the value of the index number will remain the same in whatever units the prices of the commodities are quoted.
• It does not need the quantities consumed in the current year.

Demerits

The chief demerits of this method are as follows:

• It assumes the quantities consumed in the base year to be the quantities consumed in the current year. This assumption may not hold good in all the cases. This is totally a wrong expectation particularly when the prices of elastic goods rise or fall. In such cases, people decrease, or increase the quantities of their consumption in response to the increase, or decrease in the prices respectively.
• It has an upward bias in weighting the commodities. When with the rise in the prices people reduce their quantities of consumption, the weights remain fixed being assigned on the basis of the quantities of the base year. As such, this method unnecessarily boosts up the values of the index number which is a matter of upward bias.
• It does not permit the use of any other average viz. geometric mean, median etc., than the arithmetic average only.
• It does not satisfy the time reversal test, factor reversal test, and circular test of consistency in ht index number formulae.
• It does not make use of the quantities of the current year, even if, the data in respect therefore are available.