Answer to Question #271862 in Microeconomics for kalehiwot

Question

1. Find the MU_x , MU_y , and MRS equations for each of the following utility functions. Which of the below utility functions exhibit diminishing MRS? (That is, which of the below yield convex indifference curves?).

a.      U = x^0.6y^0.4.

b.     U = x² + y²       x,y>0.

c.      U = 2x + 4y.

d.     U = x²y².

e.      U = x^ay^b

Answer 1

$M_x=2,~M_y=4,\\M_x=2x,~M_y=2y,$

$M_x=2xy^2,~M_y=2x^2y,$

$M_x=ax^{a-1}y^a,~M_y=ax^ay^{a-1},$

$M_x=0.6\frac{y^{0.4}}{x^{0.4}},~M_y=0.4\frac{x^{0.6}}{y^{0.6}}.$