Given the utility function $U(F,G)=FG^2$, find the MRS

Question

Intermediate Micro. My understanding for MRS conversions is that you find the derivative of each variable and place the former over the latter. That then in this case yields $\frac{1}{2G}$? Is this correct or is my logic misplaced here?

Answer 1

In general you are right, but your (partial) derivatives seem not right.

$MRS =\frac{U_F(F,G)}{U_G(F,G)}$

$U_F(F,G)=G^{2}$

$U_G(F,G)=2F\cdot G^{}$

$\frac{U_F(F,G)}{U_G(F,G)}=\frac{G^{2}}{2F\cdot G^{}}=\frac{G}{2F}$

Is it comprehensible ? If not, feel free to ask.