Q: Find the MUx and the MRS at (3,2) for
1) u(x,y)=x3y and 2) u(x,y)=min(2x,y)
A: 1) MUx=dU/dx=3x2y=3*32*3=81.
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.