Answer to Question #125557 in Microeconomics for umer

Question

If Maria’s utility function is U = A Xayb what is his marginal utility functions for X and Y? Find the MRS between x and y.

Answer 1

His marginal utility functions for X and Y are:

$MU(X) = U'(X) = A×a×X^{a - 1}×Y^b.$

$MU(Y) = U'(Y) = A×b×X^a×Y^{b - 1}.$

$MRS(XY) = MU(X)/MU(Y) = \frac{a×X^{a - 1}×Y^b} {b×X^a×Y^{b - 1}}$