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Convex Programming
Published in Prem K. Kythe, Elements of Concave Analysis and Applications, 2018
5.10. The Constant Elasticity of Substitution (CES) production function is defined by q=A[αK-β+(1-α)L-β]-1/β, $$ \begin{aligned}q=A\big [\alpha K^{-\beta }+(1-\alpha ) L^{-\beta }\big ]^{-1/\beta }, \end{aligned} $$
The Effects of Technological Change
Published in Keith Norris, John Vaizey, The Economics of Research and Technology, 2018
Both criteria of neutrality yield the same result only in one special circumstance—when the elasticity of substitution between capital and labour is unity. That this is necessarily the case is best seen by examining the effect of technical progress on factor shares. Assume a constant labour force. If technical progress is Hicks neutral, then clearly the distribution of income must be unchanged, because at the same capital-labour ratio the ratio of the profit rate to the wage rate (as given by the respective marginal productivities, assuming perfect competition) remains unaltered. By Harrod neutrality, with a given labour force, at the same profit rate (π), the capital-output ratio (K/X) is constant. Thus, π(K/X), which is capital’s share of the national income, is constant. Thus, we are looking at two situations which have the same distribution and the same labour force, but in the latter the capital stock is greater. In the first case, the capital stock was constant; in the latter case it increased in the same proportion as output. With a constant labour force the two situations give the same distribution with different levels of the capital stock. Thus, the elasticity of substitution between capital and labour is unity, QED. The only production function which has a constant elasticity of substitution of unity over the whole of its range is the Cobb–Douglas production function, which partly explains its popularity in econometric work, where constant elasticity of unity is an immensely helpful simplifying assumption.
Determinants of Technological Inputs
Published in Shanzi Ke, Beyond Capital and Labor, 2018
Christenson, Jorgenson, and Lau (1973) proposed that transcendental logarithmic production function (Translog) is the most general functional form that can provide a non-linear local fit to any production frontier. Both Cobb-Douglas (C-D) and constant elasticity of substitution (CES) production functions are special cases of the Translog production function. The Translog function requires the least economic and technical assumptions compared with other functional forms. More and more empirical studies employ this technique to examine input-output technological relationship. Nevertheless, few have ever mentioned any shortcomings of the Translog function in practice.
Customer and employee perceptual congruence in service co-production
Published in Quality Management Journal, 2019
Ahmet Semih Ozkul, Uzay Damali, Anup Menon Nandialath, Andrew Stapleton
Investigating perceptual biases in conjunction with service design may provide a more complete understanding of how to achieve perceptual congruence. Service design may determine: 1) the interaction level between customer and employee during the co-production; and 2) the desired customer and employee input work-allocation level. Prior research used constant elasticity of substitution (CES) functions to calculate the output through interaction and customer work-allocation level (Bhattacharyya and Lafontaine 1995; Adams 2006; Roels 2014; Karmarkar and Roels 2015). However, none of these co-production functions considered perceptual biases.