Question

Find the elasticity of sustitution for the production function Q=√LK

Answer 1

Q = L^0.5K

Elasticity of substitution ($\alpha$) = $\frac{percentage change in K/L}{percentage change in MRTS}$

% change in K/L: = ${dIn(K/L)}$

MRTS: =$\frac{MPL}{MPK}$

$MPL=\frac {\delta Q}{\delta L}=0.5L^{-0.5}K$

 $MPK=\frac{\delta Q}{\delta K }=L^{0.5}$

$MRTS=\frac{0.5L^{-0.5}K}{L^{0.5}}=\frac{0.5K}{L}$

$\alpha$ = $\frac{dIn(0.5K/L)}{dIn(0.5K/L)}$

$\alpha$ = 1