Suppose that your tastes over coke(X1) and burgers(X2) can be summarized by the utility function: u(X1, X2) = (X12X2)1/3. (a) Calculate the optimal quantity of coke and burgers' consumption as a function of P1, P2 and I. (b) 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? (c) Using your answer, show that both coke and burgers are normal goods when your tastes can be summarized by this utility function. (d) Suppose the price of coke goes up to $4. Illustrate your new optimal bundle and label it, C. (e) How much coke and burgers 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 coke as you were before(at your optimal income of $180)? Illustrate this as bundle B. (f) How large was your salary increase in the previous part? (g) Now suppose the price of burgers (P2) falls to $5 (and suppose the price of coke 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. (h) Calculate the income effect and the substitution effect (Hicksian) for both burgers and coke consumption from this change in the price of burgers. Illustrate this in your graph. (i) True or False: Since income and substitution effects point in opposite directions for coke, coke must be an inferior good. Explain.
Suppose that your tastes over coke(X1) and burgers(X2) can be summarized by the utility function: u(X1, X2) = (X12X2)1/3.
(a) Calculate the optimal quantity of coke and burgers' consumption as a function of P1, P2 and I.
(b) 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?
(c) Using your answer, show that both coke and burgers are normal goods when your tastes can be summarized by this utility function.
(d) Suppose the price of coke goes up to $4. Illustrate your new optimal bundle and label it, C.
(e) How much coke and burgers 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 coke as you were before(at your optimal income of $180)? Illustrate this as bundle B.
(f) How large was your salary increase in the previous part?
(g) Now suppose the price of burgers (P2) falls to $5 (and suppose the price of coke 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.
(h) Calculate the income effect and the substitution effect (Hicksian) for both burgers and coke consumption from this change in the price of burgers. Illustrate this in your graph.
(i) True or False: Since income and substitution effects point in opposite directions for coke, coke must be an inferior good. Explain.
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