The choice of CES production techniques and balanced growth

We show that allowing firms a choice of CES production techniques (via the distribution parameter between capital and labor) can result in a new class of production functions that produces short-run capital-labor complementarity but yields a long-run unit elasticity of substitution. This is shown to occur if we provide a mathematical framework for this choice that maintains strict essentiality of the production process and satisfies the requirement of unit-invariance. The class of production functions derived are consistent with a balanced growth path even in the presence of capital-augmenting technical progress. The approach yields a simple yet powerful way of introducing CES-type production functions in macroeconomic models.