Question

# 3. Connie has a monthly income of $200, which she allocates between two goods: meat and potatoes.

a)

Suppose meat costs $4 per pound and potatoes cost $2 per pound. Draw her budget constraint.

b) Suppose also that her utility function is given by the equation u(M, P) = 2M + P. What combination of meat and potatoes should she buy to maximize her utility? (Hint: Meat and potatoes are perfect substitutes.)

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c) Connieís supermarket has a special promotion. If she buys 20 pounds of potatoes (at $2 per pound), she gets the next 10 pounds for free. This o§er applies only to the Örst 20 pounds she buys. All potatoes in excess of the Örst 20 pounds (excluding bonus potatoes) are still $2 per pound. Draw her budget constraint.

d) An outbreak of potato rot raises the price of potatoes to $4 per pound. The supermarket ends its promotion. What does her budget constraint look like now? What combination of meat and potatoes maximizes her utility?

4. Claraís utility function is U(X, Y) = (X + 2)(Y + 1), where X is her consumption of good X and Y is her consumption of good Y.

a) Write an equation for Claraís indi§erence curve that goes through the point (X, Y) = (2,8). On a graph below, sketch Claraís indi§erence curve for U = 36.

b) Suppose that the price of each good is 1 and that Clara has an income of 11. Draw in her budget line. Can Clara achieve a utility of 36 with this budget? c) At the commodity bundle, (X, Y), Önd the Claraís marginal rate of sub-

stitution of Y for X, as a function of X and Y.

d) Solve for these two equations for the two unknowns, X and Y.

5.Donald Fribble is a stamp collector. The only things other than stamps that Fribble consumes are Hostess Twinkies. It turns out that Fribbleís prefer- ences are represented by the utility function u(s, t) = s + ln t where s is the number of stamps he collects and t is the number of Twinkies he consumes. The price of stamps is ps and the price of Twinkies is pt. Donaldís income is m.

a) Write down the optimal condition of this consumer:

b) Using the equation you found in the last part to show that if he buys both goods, Find the Donaldís demand function for Twinkies.

c) Notice that for this special utility function, if Fribble buys both goods, then the total amount of money that he spends on Twinkies has the peculiar property that it depends on only one of the three variables m, ps and pt. Write down the variable without explaining.

d) Since there are only two goods, any money that is not spent on Twinkies must be spent on stamps. Find an expression for the number of stamps he will buy if his income is m, the price of stamps is ps and the price of Twinkies is pt .

e) Donaldís wife complains that whenever Donald gets an extra dollar, he always spends it all on stamps. Is she always right? Explain brieáy.

6. David goes to the supermarket. He sees that bags of potato chips are labeled ìbuy 3 get 1 free.îAssume that he has an income of $300 to spend on potato chips and other goods, the price of other goods is $10, and the price of a bag of potato chips is $20.

a) Draw Davidís budget constraint.

b) Suppose that David would purchase 2 bags of potato chips if there was no ìbuy 3 get 1 free.îWould he buy more than 2 bags when there is ìbuy 3 get

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1 free?îIs it possible that he would buy less than 2 bags when there is ìbuy 3 get 1 free?îExplain.

c) Suppose that David would purchase 4 bags of potato chips if there was no ìbuy 3 get 1 free.îWould he buy more than 4 bags when there is ìbuy 3 get 1 free?îIs it possible that he would buy less than 4 bags when there is ìbuy 3 get 1 free?îExplain.

7. Suppose a new technique for studying economics is invented, and that it really works; that is, it really does increase a studentís economics exam score for any given number of hours of studying.Assuming that Peter studies only two subjects: economics and physics. Is it possible that Peterís economics exam score decreases despite using the new technique? Explain.

(Hint: To answer this question, assume the student has preference over his ìeconomics scoreî and ìphysics scoreî and that the score of each subject increases linearly in the hours he spends on that subject. His budget constraint captures his allocation of a Öxed amount of time spent on these two subjects.)

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