Return to the case of our beer and pizza consumption from end-of-chapter exercise 6.3.
A. Again suppose you consume only beer and pizza (sold at prices p1 and p2 respectively) with an exogenously set income I . Assume again some initial optimal (interior) bundle A.
(a) In 6.3A (b), can you tell whether beer is normal or inferior? What about pizza?
(b) When the price of beer goes up, I notice that you consume less beer. Can you tell whether beer is a normal or an inferior good?
(c) When the price of beer goes down, I notice you buy less pizza. Can you tell whether pizza is a normal good?
(d)When the price of pizza goes down, I notice you buy more beer. Is beer an inferior good for you? Is pizza?
(e) Which of your conclusions in part (d) would change if you knew pizza and beer are very substitutable?
B. Suppose, as you did in end-of-chapter exercise 6.3B that your tastes over beer (x1) and pizza (x2) can be summarize by the utility function u(x1,x2)= x12 x2. If you have not already done so, calculate the optimal quantity of beer and pizza consumption as a function of p1, p2 and I .
(a) Illustrate the optimal bundle A when p1=2, p2=10 and weekly income I=180. What numerical label does this utility function assign to the indifference curve that contains bundle A?
(b) Using your answer above, show that both beer and pizza are normal goods when your tastes can be summarized by this utility function.
(c) Suppose the price of beer goes up to $4. Illustrate your new optimal bundle and label it C.
(d) How much beer and pizza would you buy if you had received just enough of a raise to keep you just as happy after the increase in the price of beer as you were before (at your original income of $180)? Illustrate this as bundle B.
(e) How large was your salary increase in (d)?
(f) Now suppose the price of pizza (p2) falls to $5 (and suppose the price of beer and your income are $2 and $180 as they were originally at bundle A.) Illustrate your original budget, your new budget, the original optimum A and the new optimum C in a graph.
(g) Calculate the income effect and the substitution effect for both pizza and beer consumption from this change in the price of pizza. Illustrate this in your graph.
(h) True or False: Since income and substitution effects point in opposite directions for beer, beer must be an inferior good.