ELASTICITY OF SUPPLY AS A DETERMINANT OF DISTRIBUTION 115 
divergent rates of change in the total product which follow an 
alteration in the physical quantity of the factors, may be so 
equated as to be reduced to a common function. How, in other 
words, can the production of potatoes, copper ore, loaves of 
bread, and neckties be reduced to common units in which we have 
different technical coefficients of production? This, however, can 
be effected by computing index numbers of production in which 
the quantities of each product, weighted by their values, are 
reduced to relatives. If the change is to be studied over a 
period of time, this general index of production, similar to those 
constructed by the Federal Reserve Board and the Harvard Com- 
mittee on Economic Research, will measure sufficiently well what 
we desire. And if it be objected that the relative values will 
change from year to year and that consequently an index based 
on fixed weights will be wrong, it can be shown that Professor 
Irving Fisher has eliminated this difficulty in his “ideal” index 
number where he commends the use of the geometrical average of 
the index of a commodity in a given year weighted by its 
value in the base year multipled by the index for the given year 
weighted by the values of the given year. 
In this way a satisfactory physical index of general production 
can be secured to measure the physical effects of altered quantities 
of the factors. Within these physical outputs, of course, produec- 
tivity will be measured in terms of value, but for the society as 
a whole we can measure fairly accurately the productivity as a 
whole. Even here, however, there will be difficulties in taking into 
account (1) the relative degree of fabrication in manufacturing 
at different intervals, and (2) the relative amount of services 
supplied at differing periods. 
3. The relative amount of labor, capital and imputed services 
of natural resources which are contained in the commodities upon 
which laborers expend their wages as compared with the relative 
quantities of these factors which are consumed by the recipients 
of interest and of rent, also affects the final apportionment, 
of the product to the factors of production. It is important 
therefore, to trace the effects of consumption as well as of pro- 
* See Fisher, The Making of Index Numbers (1st edition), p. 482. 
The formula is: 
V Zqipe  Zqip, 
— ¥ s——— 
Sqpe ZqQop: