Q2

Q: Find the MUx and the MRS at (3,2) for

1) u(x,y)=x^{3}y and 2) u(x,y)=min(2x,y)

A: 1) MUx=*d*U/*d*x=3x^{2}y=3*3^{2}*3=81.

MRS=MUx/MUy= 3x^{2}y/x^{3}=3y/x=3*3/3=3

2) MUx=0. We know this because u(3,2)=min(2*3,2)=min(6,2)=2. The person already has excess x. Consuming more x would not increase utility as it is the y=2 that is keeping utility at a level 2. Since we are on the horizontal part of the IC, we know the MRS=MUx/MUy = 0/+ = 0.