Question

What is his marginal rate of substitution between X =3 and Y=4? If A=1, a = 0.4 and b =
0.5.

Answer 1

If the utility function is $U = AX^aY^b$ , then marginal utility functions for X and Y are:

$MU(X) = U'(X) = A×a×X^{a - 1}×Y^b.$

$MU(Y) = U'(Y) = A×b×X^a×Y^{b - 1}.$

$MRS(XY) = MU(X)/MU(Y) = \frac{a×X^{a - 1}×Y^b} {b×X^a×Y^{b - 1}} = \frac{aY}{bX} = \frac{0.4\times4}{0.5\times3} = 1.067.$