The Index-Number Problem and Its Solution pp 102-103 | Cite as

# Banerjee’s Factorial Index Numbers

Chapter

## Abstract

The underlying idea of Banerjee’s so-called factorial approach to the construction of index numbers and the index numbers of price and volume based on them should be Forming (as in factorial design analysis) the products and dividing them by \({V_0} = P_0^*Q_0^* = \Sigma P_0^iQ_0^i\) Banerjee then concludes that the aggregate price and volume indices should be such that It is at this point that it becomes clear that the underlying idea of the factorial approach is erroneous, because there exist no

^{1}appears to be that if commodity aggregates, like single commodities, had a price measure and a volume measure of their own, then these measures (which we shall denote by symbols with an asterisk) should be such that$$P_j^*Q_k^* = \Sigma P_j^iQ_k^i\quad \left( {j,k = 0,1} \right)$$

$$P = P_1^*/P_0^*\;and\;Q = Q_1^*/Q_0^*$$

$$\begin{gathered}
\left[ {P_1^* + P_0^*} \right]\left[ {Q_1^* + Q_0^*} \right] = a \hfill \\
\left[ {P_1^* - P_0^*} \right]\left[ {Q_1^* - Q_0^*} \right] = b \hfill \\
\left[ {P_1^* + P_0^*} \right]\left[ {Q_1^* + Q_0^*} \right] = c \hfill \\
\left[ {P_1^* - P_0^*} \right]\left[ {Q_1^* - Q_0^*} \right] = d \hfill \\
\end{gathered}$$

$$P_{j}^{*}Q_{k}^{*}=\Sigma P_{j}^{i}Q_{k}^{i}\quad \left( {j,k=0,1} \right)$$

*P*,*Q*pair that can satisfy simultaneously all four of these relations.### Keywords

alVo## Copyright information

© G. Stuvel 1989