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Existence of a Real ValueAdded Function
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approximation assumed assumption average capital and labor capital services Chapter classical cost function coefficients concave concave function constant constraint continuously differentiable convex convex function defined by equation demand equations demand functions Diewert disembodied technical change divisia index duality econometric elasticity of substitution electricity embodied technical change empirical error estimates ex post factor augmenting fixed fuel functional form given gross output homothetic implies indirect utility function industry input prices intermediate inputs linear homogeneous marginal products McFadden measure neoclassical non-homothetic non-negative null hypothesis observed output price parameters partial derivatives plant primary inputs problem production function production possibilities profit function Proof putty-clay quasi-concave rate of return real value-added Regression regulated firm respect restrictions returns to scale sample satisfies Section statistic Table technical progress translog translog cost function unit utility maximization problem value-added function vector vintage weakly separable zero