Question
For the CES production function \(Q=A[\delta K^{-\rho}+(1-\delta)L^{-\rho}]^{-1/\rho}\), where \(A>0,\ 0<\delta<1\), what is the elasticity of substitution when \(\rho=-1\)?
The correct answer is
Infinite
At \(\rho=-1\), the function becomes \(Q=A[\delta K+(1-\delta)L]\). The inputs are perfect substitutes, so the elasticity of substitution is infinite. This is the limiting case of \(\sigma=1/(1+\rho)\).
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