Tecnologia cristalizada e produtividade total dos fatores

Suppose that the production, y = f (x1, x2,..., xs ) , is known. It says that we are able to know for each value of the input vector, 1 2 , ,..., s x x x , the correspondent value of y. Or yet production growth occurs as consequence of movement along the production frontier, and it requires a different combination of inputs, and consequently, a higher or a smaller expenditure. Another representation of the production structure is, 1 2 ( , ,..., , ) s y = f x x x t , where t is non negative real number. Now each set of 1 2 , ,..., s x x x gives a different y as t varies. Or, it is possible to achieve a higher level of production with no additional cost. A question comes to mind: can the real world (or the data) say which one of the two representations has a better descriptive power? The answer is no. Or yet, the real world cannot distinguish between embodied and disembodied technology in a sense that will be introduced below. We will not use directly the concept of production function to establish the model appropriate to test embodied technology against the disembodied one. In its place, the rates of growth of products and inputs are instrumental.