Problem Set 1

Problem Set 1 - Econ 330 – Economic Behavior and...

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Unformatted text preview: Econ 330 – Economic Behavior and Psychology Spring 2010 Professor Sydnor Problem Set 1 Problem 1: When some stores started introducing charges for credit‐card transactions, credit‐card companies lobbied hard to have stores call the credit‐card price the regular price and the difference a “cash rebate”, rather than call the cash price the regular price and the difference a “credit‐card surcharge.” Explain how this relates to the concepts we have discussed so far in class. Problem 2: Tim and Randy both have simple “prospect‐theoretic” preferences for money (m) relative to their reference point (r). Both have preferences of the following form: V(m, r) = m‐r when m ≥ r and V(m, r) = ‐λ(r‐m) when m < r. a) Do these preferences exhibit loss aversion? What are the conditions (if any) on the parameters for which the model exhibits loss aversion? b) Do these preferences exhibit diminishing sensitivity? Suppose that both of them currently have $50,000 and are sitting down to lunch with their friend Samuel Paulson. Samuel Paulson offers them each a gamble based on the flip of a fair coin. If the coin comes up heads they will owe Samuel $100 and if the coin comes up tails Samuel will pay them $150. c) Both Tim and Randy turn down Samuel’s offer. What have we learned about the range of λ? Now Samuel offers them the same gamble, but played out twice in succession (i.e., flip the coin once and then again). So, for example, if it comes up heads and then tails, Samuel would owe them $50. The money will be paid out after the two flips of the coin. Randy shouts “What difference does that make? I did not want to play one round of this bet, so I’m not even going to think about it at all; I won’t play 2 or 3 or 4 or whatever number of bets.” So Randy is Narrow Bracketing. Tim, however, says “Hold on a minute. I’m going to calculate the possible outcomes from this combined gamble. I don’t like 1 flip of the coin, but I might like two flips.” So Tim is Broad Bracketing. d) Tim does this calculation and then responds that he still does not want to play. What have we learned about the range of Tim’s λ? (Notice that we have learned nothing new about Randy because he is Narrow Bracketing). Samuel now offers them the same gamble again, but played out 3 times in succession (i.e., flip the coin three times in a row). The money will be paid out after the three flips of the coin. Randy screams “Leave me alone!” Tim says, “Ok, let me now calculate the possible outcomes from 3 independent trials of this gamble and I’ll consider whether I want to take it.” Econ 330 – Economic Behavior and Psychology Spring 2010 Professor Sydnor e) Tim now decides to accept the gamble if they play 3 times. What have we learned about the range of Tim’s λ? f) Could we learn anything else about the range of Tim’s λ by offering him the same gamble with more flips of the coin? Problem 3: Jane and Melody frequently play chess together and to make it interesting, they sometimes play for money. They just had a $100 bet on a chess game and Jane lost and is now reeling from the fact that she just lost $100. Suppose that Jane has the following preferences for money relative to her reference point (which in this case is the amount of money she had before she started playing the game with Melody). V(m, r) = m‐r when m ≥ r and V(m, r) = ‐λ(r‐m) when m < r. Jane is considering challenging Melody to another match, Double or Nothing (i.e., another $100 bet). a) Given her preferences, how high must the probability (p) that Jane thinks she’ll beat Melody be in order for Jane to levy the challenge? b) Does the answer to (a) depend on λ? Explain in intuitive terms why it does or does not depend on λ. Now suppose instead that Jane’s preferences are given by: V(m, r) = √ when m ≥ r and V(m, r) = ‐λ√ when m < r. c) Give a verbal description of how these preferences differ from those above and what it means for the psychology of how Jane reacts to changes in money. d) Given these new preferences, how high must the probability (p) that Jane things she’ll beat Melody be in order for Jane to levy the challenge? e) How does this problem relate the “long‐shot bias” in end‐of‐the‐day betting at horse races? Econ 330 – Economic Behavior and Psychology Spring 2010 Professor Sydnor Problem 4 Consider two gambles: Gamble A is a 50/50 chance to lose $50 and a 50/50 chance to gain $55 Gamble B is a 50/50 chance to lose $500 and a 50/50 chance to gain $4000 In class I argued that the tendency for people to reject small‐scale gambles like Gamble A is inconsistent with the expected‐utility‐of‐wealth model because in that model if someone turns down Gamble A, they would also be predicted to turn down pretty obviously favorable gambles like Gamble B. In this problem I want you to create a simple Excel Sheet (or other program you like to use) to verify this. Specifically, assume that Bob has a starting wealth level of $10,000. Also assume that Bob maximizes his expected utility of wealth and that his utility‐of‐wealth function is given by: u($X) = Here r is the risk‐aversion parameter. The higher r is, the greater is risk aversion. (Note that in the special case where r = 1, this function is the natural log, but you can largely ignore that for this problem if you are moderately clever) a) Find the minimum value for r that makes Bob prefer staying at his wealth level of $10,000 to taking Gamble A. (Hint, it will be greater than 1 – feel free to use only one decimal place) b) Verify that if Bob’s level of r is as in (a) that he would turn down Gamble B. Do this by calculating the expected utility of Gamble B and comparing it to the expected utility of Gamble A with the level of r you found in part (a). You could also find the maximum r that Bob could have such that he would accept Gamble B and show that it’s less than the r you found in part a. ...
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