Curvatures of Productivity, Elasticities of the Output and Stages of Production

As a rule, the concept of marginal productivity is used in order to determine the efficient distribution of incomes or optimal levels for inputs allocations in the context of diminishing marginal returns. But the definition of the concept of the endogenous economic growth imposed the relaxation of assumptions on the feature of the marginal returns, admitting that it is possible, in certain situations, to deal with both increasing and decreasing marginal returns. This paper defines a neoclassical production function with one input, which admits both the increasing and decreasing marginal returns and, in certain manner, the existence of the Jevons paradox. The respective production function is then used for the analysis of the curvature of the marginal and average productivity and of the elasticity of the output. On this basis, we are able to reconfirm the neoclassical assumptions on the size of the elasticity of the output in the context of the decreasing marginal returns and output maximization, on the one hand, and to show that in the context of a convex curvature and of increasing of both average and marginal productivity the elasticity of the output is higher than 2, on the other hand. Also, it is propsed a redefinition of the notion of stages of production considering the features of the curvature of the average productivity and of the elasticity of the output.