Inada conditions

As Inada conditions are referred to in the neoclassical production and growth theory several conditions that are usually placed on the production functions used. The name goes back to an article by the Japanese economist Ken -Ichi Inada from 1963, in which he formulates this explicitly for a growth model.

Importance

Be a production function, which represents the use of capital and labor inputs. Then the Inada conditions imply (in the narrow sense) that the marginal product of each factor of production converges to infinity when you can only strive each factor input to zero; can be added to each factor input, however, to tend to infinity, so the marginal product of the factor converges to zero. Formally considered so

Respectively

A typical, useful for technical purposes, interpretation of these conditions is, for example, that for a given technology, in an economy, the output can not be increased by the labor input is increased more and more.

It can be shown that the performance of the Inada conditions imply in terms of the production function, that this must be asymptotically by the Cobb -Douglas type.

The term " Inada conditions" is used here out of focus in the literature; the majority of authors is limited to the excess demands, others expect the Inada conditions beyond other classically assumed ( and, indeed, Inada inherited ) conditions, such as the assumption of decreasing marginal productivity (see also the following section ).

Implications

Assuming, as is typically assumed for production functions that both input factors have a positive but diminishing marginal productivity, so that:

Respectively

And that the production function has constant returns to scale (homogeneous of degree = one):

Then follows from the above Inada conditions, moreover, that each employed factor essential (also essential) is. What this means is that an economy in a state in which there is either no capital or no work, can generate any output. Formally: