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The main aim of this paper is to prove the existence of a new production function with variable elasticity of factor substitution. This production function is a more general form which includes the Cobb-Douglas production function and the CES production function as particular cases. The econometric estimates presented in the paper confirm some other results and reinforces the conclusion that the sigma is well-below the Cobb-Douglas value of one.doi:10.2139/ssrn.3241315 fatcat:j3he6reqyzbijjcnrjqnwsni3a