The Law of Diminishing Returns and the Generalized CES Production Function

There are two troubling and largely unrecognized implications of the generalized CES production function when there are increasing returns to scale and the elasticity of substitution (𝜎) exceeds one: (1) under these conditions the CES production function is always inconsistent with the law of diminishing marginal returns to either labor or capital and (2) the marginal product of labor (capital) always approaches infinity as labor (capital) approaches infinity. To avoid these two implications one must restrict the parameter values of the CES production function to either not allow for increasing returns to scale or to require that σ