Jack makes his consumption and saving decisions two months at a time. His income this month is $1,000, and he knows that he will get a raise next month making his income $1,050. The current interest rate (at which he is free to borrow or lend) is 5 percent. Denoting this month's consumption by x and next month's by y, for each of the following utility functions state whether Jack would choose to borrow, lend, or do neither in the first month.
a) U(x, y) = xy2, MUx = y2, MUy = 2xy
b) U(x, y) = x2 y, MUx = 2xy, MUy = x2
c) U(x, y) = xy, MUx = y, MUy = x