A Modification of the CES Production Function to Allow for Changing Returns to Scale over the Function - Soskice, David (The Review of Economics and Statistics, 1968)
originally proposed by Arrow, Chenery, A Minhas and Solow, the CES function was constrained to constant returns to scale. It has since been generalised to allow for any degree of homogeneity in the inputs. But the function is still constrained: if returns to scale are a when output is low, they are equally a when output is high. It is shown later in this paper that if this assumption is untrue, if what may be called point returns to scale are themselves functionally related to output, a common procedure for estimating the elasticity of substitution will generally be inconsistent, even if it would not otherwise have been so. To prove this, a modified CES function is derived in which point returns to scale are functionally related to output.