Question

Supose the consumer`s utility function is given by U= 10X1/2Y1/4. Compute both MRSxy and MRSyx. Is there any difference between the two?

Answer 1

Solution:

U = 10X^1/22Y^1/4

MRSxy = $\frac{MUx}{MUy}$

MUx = $\frac{\partial U} {\partial X}$ = 5X^-1/22Y^1/4

MUy = $\frac{\partial U} {\partial Y}$ = 2.5X^1/22Y^-3/4

MRSxy = $\frac{5X^{-1/2}2Y^{1/4} } {2.5X^{1/2}2Y^{-3/4}}$ = $\frac{5Y } {2.5X}$

MRSxy = $\frac{5Y } {2.5X}$

 

 

MRSyx = $\frac{MUy}{MUx}$

MUy = $\frac{\partial U} {\partial Y}$ = 2.5X^1/22Y^-3/4

MUx = $\frac{\partial U} {\partial X}$ = 5X^-1/22Y^1/4

MRSyx = $\frac{2.5X^{1/2}2Y^{-3/4} } {5X^{-1/2}2Y^{1/4}} = \frac{2.5X } {5Y}$

MRSyx = $\frac{2.5X } {5Y}$

 

Both MRS are different since they are showing different values and hence will produce different results.