We provide a general theoretical characterization of how firms' technology choice on a technology frontier determines the long-run elasticity of substitution between capital and labor. We show that the shape of the frontier determines factor shares and the elasticity of substitution between capital and labor. If there are adjustment costs to technology choice, the short- and long-run elasticities differ, with the long-run always higher. If the technology frontier is log-linear, the production function becomes Cobb-Douglas in the long run but, consistent with empirical evidence, short-run dynamics are characterized by gross complementarity. The approach is easily implementable and yields a powerful way to introduce CES-type production functions in macroeconomic models. We provide an illustration within an estimated dynamic general equilibrium model and show that the use of our production technology provides a good match for the short- and medium-run behavior of the US labor share.
Balanced growth appropriate technology elasticity of substitution