Question

What is the marginal rate of substitution for U(x,y) = ãxy? ,ã(x+y)?

Answer 1

Aargh font didn't come out right. I meant MRS of U(x,y) = (xy)^0.5 (ie sqaure root of xy) and (x+y)^0.5.

Answer 2

Use basic calculus. MUx = .5y^.5/x^.5
MUy = .5x^.5/y^.5
MRS = MUx/MUy = y/x

take it from here