Inada conditions imply that production function must be asymptotically Cobb–Douglas

Abstract

We show that every twice-continuously differentiable and strictly concave function f : R + → R + can be bracketed between two C.E.S. functions at each open interval. In particular, for the Inada conditions to hold, a production function must be asymptotically Cobb-Douglas.

The Contribution of Human Capital towards Economic Growth in China

“…Inada included the following conditions: the function is continuously differentiable; the function is concave, that is, the derivative of the function is decreasing; the limit of the derivative towards 0 is positive infinity; and the function is increasing in x. Barelli and deAbreu Pessôa (2003) showed that for the Inada conditions to hold, the elasticity of substitution is asymptotically equal to 1. However, the Inada conditions only apply fully if the Cobb-Douglas production function is the appropriate function in congruence with the empirical facts.…”

The Role of Energy in the Industrial Revolution and Modern Economic Growth

“…However, in general, CES functions other than the Cobb-Douglas function do not satisfy the Inada conditions (Barelli and de Abreu Pessoa, 2003). It is possible for extreme parameter values -low savings rate, high depreciation rates, high levels of β and low levels of σ -that (8) is not met neither near the origin nor for any positive value of K so that there is no positive equilibrium level of capital.…”

Bad Investments and Missed Opportunities? Postwar Capital Flows to Asia and Latin America

“…Identification of the wedges is quite intuitive. The international wedge, for example, is determined by differences in consumption growth rates across countries from equation (3). Likewise, the capital wedge is identified by differences in estimated marginal products of capital (from capital/output ratios) from growth rates of consumption within a country (2), and the labor wedge is determined from a comparison of hours worked and consumption levels within a country (1).…”

“…Note that the competitive equilibrium's international wedge (see Figure7) corresponds to the growth rate of the pseudo planners wedge or what we call cumulative international wedge (see Figure 6). 3 Since all wedges are relative to the rest of the world, there are only two lines in these Figures.…”