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Consider a CES production function $Y=f(K,L)$ with elasticity of factor substitution $\sigma>0$.

The substitution effect of higher real wages naturally implies a shift along the isoquant to more $K$. The rise in costs will reduce output. The total effect of $w \uparrow$ on $Y$ and $K$ is the sum of this substitution and output effect.

I'm interested in the link between the value of $\sigma$ and the strength of these two effects. Does anyone know a good reference, or lecture notes on the algebra of these effects in the CES context?

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