# Using total differential to find the marginal rate of substitution

• Mar 11th 2010, 10:01 AM
ihatemath09
Using total differential to find the marginal rate of substitution

Consider the utility function U(x, y) = xy + y.
(a) Use the total differential to find the marginal rate of substitution (MRS) between y and x.
(b) Use the MRS to show that the indifference curves are strictly convex to the origin (i.e.
show that the MRS is diminishing).
• Mar 11th 2010, 04:21 PM
matheconomics
Econ 2770
Hello

I am currently working on this exact same question .. Have you gotten anywhere with it yet?
• Mar 11th 2010, 05:20 PM
ihatemath09
unfortunately not..
I can't really spend any more time on it because i have a stats midterm tomorrow i need to study for.
hopefully someone helps us out
• Mar 14th 2010, 03:13 PM
CaesarXXIV
Quote:

Originally Posted by ihatemath09

Consider the utility function U(x, y) = xy + y.
(a) Use the total differential to find the marginal rate of substitution (MRS) between y and x.
(b) Use the MRS to show that the indifference curves are strictly convex to the origin (i.e.
show that the MRS is diminishing).

a)

dU=Ux*dx+Uy*dy=0
-Ux/Uy=dy/dx
Ux/Uy=-dy/dx= y/(x+1)

b)

Since
-dy/dx=y/(x+1)
dy/dx=-y/(x+1) since y>0, x>0 MRS is always diminishing