(Solved): Compute marginal utilities and marginal rate of substitution for each of the utility functions give ...

Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. a) \( U(X, Y)=1-e^{-a X}-e^{-b Y} \) b) \( U(X, Y)=X Y+3 X+5 Y \) c) \( U(X, Y)=\left(0.3 X^{m}+0.7 Y^{m}\right)^{\frac{1}{m}} \) d) \( U(X, Y)=\frac{X^{1-a}}{1-a}+\frac{Y^{1-b}}{1-b} \)