La ley del óptimo técnico

Abstract

The object of this article is to study the so-called Law of the Optimum Technician in relation to the continuous function of production. We presume that the production function is defined by the dimension interval of n ai<= vi <=bi, with ai>0, i=1,...,n where partial first continuous derivates are allowed, but the existence of partial second derivatives are not sought. We presume that marginal productivity x'i (vi) is first a positive monotony, increasing until it reaches a maximum, after which it is a decreasing monotony until it reaches a minimum of negative value, to later become an increasing negative monotony. Based on this we analytically deduce that the medium productivity curve xi(vi) in the different cases which may arise finally brings us to the needed condition, sufficient to fulfill the Law of the optimum technician. This is followed by a geometric interpretation of the question, and concludes by considering the special case of ai= 0.