The aggregate elasticity of factor substitution with middle products

The elasticity of substitution between factors in production relates the change in the ratio of factors used in a production process to a given change in the factor price ratio. An aggregate concept of such an elasticity relates a change in overall factor endowments to the resulting change in factor prices. For a closed economy the behavior of consumers is an important part of such an aggregate elasticity, since endowment changes can bring about changes in commodity prices and resulting adjustments to factor prices. For a small open economy, commodity prices in typical models are exogenous. In the model with middle products, all final consumer goods are non-traded, so that local consumer behavior can affect factor prices. The aggregate elasticity of substitution is shown to be an average of production elasticities and demand elasticity even for a small open economy.