A Reformulation Of The Concept Of Returns To Scale

We propose the gh-returns to scale concept which generalizes the traditional returns to scale concept. This new concept takes into account variations of all the inputs in unspecified proportions, in the evolution of production, contrary to the returns to scale concept which takes into account, only equiproportionate variations of all the inputs which lead to the implementation of production. It will appear that, when characterizing (or determining) the returns to scale (constant, increasing or decreasing), homogeneity of degree of a (production) function no longer plays the central role (except the traditional case where all the factors vary in the same proportions) it was once attributed as the nature of returns to scale can be evoked, with this new approach of unspecified variations of the proportions, whatever the degree of homogeneity of a (production) function. It will also appear that, if the producer wishes or if he is constrained to be located in a precise zone of the gh-returns to scale (for example, that of increasing gh-returns to scale, because of limited outlets or a badly filled order book), the change of its size or scale in the long run, (in case of an investment which requires capital deepening synonymous with the increase in the proportion of a factor (capital) to the detriment of the reduction in the proportion of another factor (labor)), should not be made in a hazardous way, but must rather obey specific conditions (or constraints) characterizing such a zone of the gh-returns to scale.