Question

verify maximum Q =( L ,K) subjected to c=wage×labour +interest×capital

Answer 1

Solution:

The cost-minimizing combination of capital and labor is the one where:

$MRTS_{K,L} = \frac{ MP_{L} }{ MP_{K} } = \frac{ w}{ r }$

C = W_L + rK

$\frac{ MP_{L} }{ w } = \frac{ MP_{K} }{ r } = \frac{ MP_{L} }{ MP_{K} } = \frac{ w }{ r}$

Therefore:

$MRTS_{K,L} = \frac{ w}{ r }$