Question

Q = L2 K. Calculate the elasticity of substitution

Answer 1

Q = L²K

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

% change in K/L: = ${dIn(K/L)}$

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

$MPL=\frac {\delta Q}{\delta L}=LK$

 $MPK=\frac{\delta Q}{\delta K }=L^{2}$

$MRTS=\frac{LK}{L^{2}}=\frac{K}{L}$

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

$\alpha$ = 1