Substitutive or supportive factors of production
Let's find the Marginal Product of Labor, $MP_L$:
$$
\begin{align}
MP_L \equiv \frac{\partial Y(K,L)}{\partial L} &amp;=\frac{\partial }{\partial L}\left( aK + b L^{0.5} \right) \\
&amp;= 0.5\cdot b \cdot L^{-0.5}
\end{align}
$$
Now finding $\frac{dMP_L}{dK}$ is trivial:
$$
\begin{align}
\frac{dMP_L}{dK} &amp;= \frac{d}{dK} \left( 0.5\cdot b \cdot L^{-0.5}\right) = 0
\end{align}
$$
We see that it does not depend on the capital. So a change in $MP_L$