1. Suppose using empirical evidence that you discover that a good approximation of the average U.S. consumer’s indifference curve map over the two goods Clothing per year and Food per year is as illustrated below. What might you suggest is a reasonable interpretation for such an indifference curve map?
    [ANSWER] One interpretation of this indifference curve map is that there are minimum levels of food and clothing necessary to support life. The consumer cannot trade one good for the other if it means having less than these critical levels. As the consumer obtains more of both goods, however, the consumer is increasingly willing to trade between the two goods and they start looking more and more like perfect substitutes for one another.
  1. Sam loves his manhattans made exactly to perfection according to the following family recipe: 2 oz. Whiskey, 1 tbsp. SweetVermouth, and a pinch of Angostura Bitters. If Manhattans are the only thing Sam consumes, what is Sam’s utility function?
    [ANSWER] USam = min {B, V, 1/2W} where B=bitters measured in pinches, V is vermouth measured in tablespoons and W is whiskey measured in ounces.
  1. The Wissink kids, Gerrit, Christine and Greg are trying to decide where to go to dinner one night. There are three choices: Hals Deli, Subway and Taco Bell. Gerrit says his ranking of the three, from best to worst is: Hals, Subway and then Taco Bell. Greg's preferences are: Subway, Taco Bell, and then Hals. Christine's preferences are: Taco Bell, Hals and then Subway.
  1. Gerrit proposes they take each pair of alternatives and let a majority vote determine the family preference ranking over each pair of alternatives. That is to say if “A” goes up against “B”, the alternative with more votes is preferred to the other. Determine the family ranking over each pair of alternatives based on Gerrit's proposal. Over the three alternative eateries, is this family’s ranking complete? Is this family’s ranking transitive?
  2. Christine suggests that they first decide on Hals and Subway and then put the winner up against Taco Bell. Is this a good suggestion? For whom?
  3. Greg argues that he should get to set the voting order. Why would he argue for that?
  4. Gerrit decides that if Christine is going to set the voting order, since she is the oldest and the oldest always gets to set the order, then he is going to cheat. How might Gerrit cheat and if his assumption that Greg and Christine won't cheat is correct, can be benefit from cheating?
    [ANSWER] a. Using majority voting over each pair of places we get: TB vs. H results in TB winning (Christine and Greg vote for TB over H). So: TB is preferred to H. Now consider H vs. S and you get: H is preferred to S. Now consider TB vs. S and you get that: S is preferred to TB. So the family's preferences just cycle around and around with no un-dominated choice emerging (under this method of majority rule). The family's ranking, however, is complete since we can always compare any two eateries this way. The family's ranking IS NOT transitive since TB is preferred to H and H is preferred to S but it is NOT true that TB is at least as good as S since S is preferred to TB.
    b. This is a great suggestion for Christine since they will get that H wins over S and then when we put up H against TB they get TB as the winner! She gets her best alternative. Gerrit, however, is none too pleased.
    c. If Greg gets to set the agenda, he will have the family vote on TB vs. H first and then put the winner up against S. With this agenda TB wins the first vote and S wins the second and Greg is very happy. (He who sets the agenda rules!)
    d. Assuming Christine sets the agenda and Greg and Christine behave truthfully, then Gerrit can manipulate the situation by voting for S over H in the 1st round of voting. Then S would win and go up against TB. S would win against TB and be the selected place to eat. Gerrit has altered the family choice to his middle choice, which for him is better then ending up at TB.
  1. If Jeremy’s utility function is U(B, Z) = B + ABαZβ + Z, what is his marginal utility of Z? What is his marginal rate of substitution between these two goods, B and Z?
    [ANSWER]
    MUZ = 0 + βABαZ(β-1) + 1
    Assuming “Z” is the horizontal good and “B” is the vertical good…
    MRS = MUZ/MUB = [βABαZ(β-1) + 1] / [1 + αAB(α-1)Zβ]