Graph a typical indifference curve for the following utility functions, and determine whether they have convex indifference curves (i.e., whether the MRS declines as x increases).

a. U 1x, y2 5 3x 1 y.

b. U 1x, y2 5 "x # y.

c. U 1x, y2 5 "x 1 y.

d. U 1x, y2 5 "x2 2 y2

.

e. U 1x, y2 5 xy x 1 y

.