Consider the following utility functions:
U(x, y) = xy
U(x,y) = 3x + 6y
U(x,y) = 20x1/2+ 2y
a. Fixing y at 4, what is the marginal utility of X when x is 10, 20, and 30 for each utility function?
b. Do these utility functions exhibit diminishing marginal utility of X? Explain.
c. For each utility function, calculate the marginal rate of substitution of good X for good Y (i.e. -marginal value of X, measured in units of good Y) associated with the bundle (x, y) = (10, 4).
d. Do these utility functions exhibit diminishing marginal rates of substitution? Explain.