# Thread: Using total differential to find the marginal rate of substitution

1. ## 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).

2. ## Econ 2770

Hello

I am currently working on this exact same question .. Have you gotten anywhere with it yet?

3. 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

4. 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