Wayne has $38 to spend each week on doughnuts and posters. Doughnuts (D) sell for 50 cents each and posters (P) sell for $2 each. Wayne's utility function is: U= 10D+80P-D2-2P2. Thus, the MUD=10-2D and the MUP = 80-4P.
a. If Wayne is currently consuming 2 doughnuts and 18.5 posters is he maximizing his utility? If not, what can do to increase his utility? Explain why.
b. What combination of doughnuts and posters will maximize his utility?
c. Suppose the price of posters increases to $4. Calculate the new utility-maximizing point. What happens to the individual demand curve for posters? What happens to the individual demand curve for doughnuts? Are these goods complements or substitutes? Explain.
d. Suppose instead that Wayne's income increases to $50 (price of posters = $2). Calculate the new utility-maximizing point. What happens to the individual demand curve for posters? What happens to the individual demand curve for doughnuts? Are these goods normal or inferior? Explain.