For each of the following utility functions, find the marginal utilities (MUx and MUy) and the marginal rate of substitutional between x and y (MRSxy) and explain whether MRSxy is diminishing or not.
a) u(x,y) = x1/2y
b) u(x,y) = x1/3y2/3
c) u(x,y) = x2+3y-2