Sekerka - Kyn - Hejl: Price Systems Computable from Input-Output Coefficients



7. Prices and price indices



Thus far we have assumed that the elements of vector P express the number of monetary units for each physical unit of production. The same equations are also used for finding indices of transformation from the prices currently prevailing in the national economy to computed prices. Let us call P current (empirically given) prices, P1 calculated prices, and Pi  price indices. If P > 0, then Pi can be defined:

                                Pi   =  ( P^)-1 P1              (36)

Let A be the matrix A expressed in prices P, that is,

 A      =     P^A( P^)-1         (37)

Consider N-income prices         P1   =  (1 + n*)A'P1             

This equation can be written   ( P^)-1P1   =  (1 + n*)( P^)-1A'P^( P^)-1P1

Considering eqs. (36) and (37) we can write         Pi   =  (1 + n*)A'Pi 




If we use matrices expressed in prices P, instead of those expressed in physical terms, we can calculate price indices Pi for all types of prices by this same method. Note that a different interpretation of the normalizing condition (35) is required when we calculate price indices. We require, for instance, that the volume of the gross social product .~, expressed in prices P, be the same as in prices P1:        XP1 = XP0.

If we define        V  =  XP^/ X

we can, again, write this condition      VPi = 1.









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