A consumer has a utility function given by U(x,y) = 2xy^.5

a) It is often assumed that consumer preferences exhibit diminishing marginal utility.

Explain in words what diminishing marginal utility means. Does this utility function exhibit

diminishing marginal utility? Why or why not?

b) Find the consumer's optimal choice of x and y when the consumer has an income of 180 and faces prices Px= 4 and Py=6. Illustrate the situation graphically.

c) Derive the consumer's demand function for x? (Find the optimal choice of x as a function of the price of x, income and the price of y.)

d) Is X normal or inferior? Why? What happens to the proportion of the consumer's income that is spent on x as the consumer's income increases?