Suppose a consumer’s utility function is given by U(X, Y) = X*Y. Also, the consumer has $32 to spend, and the price of X, PX = 4, and the price of Y, PY = 1.

(a) How much X and Y should the consumer purchase in order to maximize her utility?

(b) How much total utility does the consumer receive?

(c) Now suppose PX decreases to 1. What is the new bundle of X and Y that the consumer will demand?

(d) How much money would the consumer need in order to have the same utility level after the price change as before the price change?

(e) Of the total change in the quantity demanded of X, how much is due to the substitution effect and how much is due to the income effect?

(f) Sketch the graph that allows you to determine the income and substitution effects. Your graph should include the original budget constraint, the new budget constraint, and the compensated budget constraint. Also, identify the bundle the consumer chooses when facing each of these three budget constraints. Label the initial bundle A, the bundle chosen facing the new budget constraint B, and the bundle chosen when facing the compensated budget constraint C. Also, draw the indifference curve that goes through the initial bundle. You should identify two bundles on this indifference curve besides bundles A and C.