# Relationship between Elasticity of substitution of sectoral outputs and elasticity of substitution of inputs

There are two sectors Y1 and Y2.

Composite output is given by CES form -

Each sector employs Capital and Labor in combination through Cobb-Douglas Production Technology.

The paper mentions that elasticity of substitution between products will be less than one if and only if the (short-run) elasticity of substitution between labor and capital is less than one. They donot provide any motivation behind it. Why should this be true? - Any technical or non-technical explanation will be useful.