Question 1

Jim Holtzhauer is playing the tables at Vegas. He currently has $10,000, which I will denote as 10K in order to keep things simple. He is looking at a bet where with ½ chance he can win 6K while with ½ chance he will lose 2K. Jim's utility of wealth function is given by U(W) = (W)^2. (U(W) is equal to the W Squared). Based on this information, you would conclude that:

Accepted Answer

A)   Jim will not accept the gamble since he is risk averse.
B)   Jim will not accept the gamble since his expected utility from accepting the gamble is 100K^2 while the expected utility from keeping the 10K is 160K^2.
C)   Jim will not accept the gamble since his expected utility from accepting the gamble is 160K^2 while the expected utility from keeping the 10K is 100K^2.
D)   Jim's Certainty Equivalent is approximately 12.65K. D

Question 2

Suppose you have won $1,000 on a game show. In addition to these winnings, you are now asked to choose between:
Alternative 1. Gamble A: Win $1000 with 0.50 probability or Gamble B: Win $500 for sure.
On the other hand, suppose you have won $2,000 on a game show and are then asked to choose between:
Alternative 2. Gamble C: Lose $1,000 with 0.50 probability or Gamble D: Lose $500 for sure.
It is frequently observed that a majority choose Gamble B for Choice 1 while they choose Gamble C in Alternative 2.
Show that the final wealth levels are not different for the two alternatives. If the final wealth levels are not different then why do people choose Gamble B over Gamble A in Alternative 1, while they choose Gamble C over D for Alternative 2?

Accepted Answer

The final wealth levels for the two alternatives are not different. In both cases, the expected value of the gambles is the same.

For Alternative 1:
- Gamble A: Win $1000 with 0.50 probability
- Gamble B: Win $500 for sure

The expected value of Gamble A is 0.50 * $1000 = $500. So, on average, you would win $500 with Gamble A. 
The expected value of Gamble B is simply $500. So, on average, you would win $500 with Gamble B.

For Alternative 2:
- Gamble C: Lose $1000 with 0.50 probability
- Gamble D: Lose $500 for sure

The expected value of Gamble C is 0.50 * (-$1000) = -$500. So, on average, you would lose $500 with Gamble C. 
The expected value of Gamble D is simply (-$500). So, on average, you would lose $500 with Gamble D.

Since the expected values are the same for both alternatives, the final wealth levels are not different.

However, people may choose Gamble B over Gamble A in Alternative 1 because they are risk-averse. Even though the expected value is the same, the uncertainty of winning $1000 with 0.50 probability may be less appealing than the certainty of winning $500.

Similarly, people may choose Gamble C over Gamble D in Alternative 2 because they are risk-seeking. Even though the expected value is the same, the uncertainty of losing $1000 with 0.50 probability may be more appealing than the certainty of losing $500.

In both cases, people's risk preferences drive their choices, even though the final wealth levels are not different.

Question 3

Suppose Ana's current wealth (W) is $8000 and Ana obeys the principles of expected utility theory. Suppose she is offered a gamble where she can win $5000 with one-half chance but she can lose $5000 with one half-chance. Suppose her utility function is defined as U(W) = W^0.5. (The square root of her wealth). What is the expected monetary payoff of this gamble? What is the expected utility of the gamble? What is Ana's certainty equivalent? What is her risk premium? If Ana were offered this gamble, then on the basis of the utility function defined above, would she accept the gamble or would she prefer on to hang on to her $8000 endowment?

Accepted Answer

To find the expected monetary payoff of the gamble, we calculate the weighted average of the possible outcomes. The expected monetary payoff (EM) is given by:

EM = (0.5 * $5000) + (0.5 * (-$5000)) = $2500 - $2500 = $0

The expected utility of the gamble is found by calculating the utility of each possible outcome and taking the weighted average. The expected utility (EU) is given by:

EU = (0.5 * (8000 + 5000)^0.5) + (0.5 * (8000 - 5000)^0.5)
   = (0.5 * 13000^0.5) + (0.5 * 3000^0.5)
   = (0.5 * 113.86) + (0.5 * 54.77)
   = 57.43 + 27.39
   = 84.82

To find Ana's certainty equivalent, we solve for the value of the certain amount of wealth that would give her the same level of utility as the gamble. Let CE be the certainty equivalent. We solve for CE in the equation:

U(CE) = EU
CE^0.5 = 84.82
CE = 84.82^2
CE = 7189.47

The risk premium is the difference between the expected value of the gamble and the certainty equivalent. The risk premium (RP) is given by:

RP = EU - W
RP = 84.82 - 8000
RP = -7915.18

Since the risk premium is negative, Ana would prefer to hang on to her $8000 endowment rather than accept the gamble. This is because the expected utility of the gamble is lower than the utility of her current wealth, indicating that she would be better off sticking with her current wealth rather than taking the gamble.

Question 4

Suppose your current wealth (W) is $10,000. Suppose you are offered a gamble where you can win $4000 with one-half chance but you can lose $4000 with one half-chance. Suppose your utility function is defined as U(W) = W^0.5. (The square root of your wealth). To you, the Certainty Equivalent (CE) of this gamble is approximately:

Accepted Answer

A)   9582.5.
B)   100.00.
C)   10,000.
D)   417.6.

Question 5

Consider two sides negotiating over how to split a surplus. It is more likely that they will arrive at a mutually agreeable outcome if the two sides:

Accepted Answer

A)   Are realistic and adopt a gain frame.
B)   Are over-confident and adopt a gain frame.
C)   Are realistic and adopt a loss frame.
D)   Are over-confident and adopt a loss frame.

Question 6

Ken Jennings has just been offered a job with a start-up company. The job pays $30,000 guaranteed per year. On top of that that there is a ½ probability that he can get a $50000 performance bonus making a total of $80,000. Ken operates under the assumptions of expected utility theory and in general, has a strong preference for a job that pays a fixed amount per year. Ken's utility of wealth function is given by U(W) = W^0.5. (U(W) is equal to the Square Root of W). Show that if Ken has a choice between this job and another job that pays $60,000 per year then he will choose the other job over the job with the start-up company.

Accepted Answer

The answer of Ken Jennings has just been offered a...

Question 7

Assume, Elizabeth's utility function is: U(W) = W^0.5 and she operates under the tenets of expected utility theory. She is considering two job proposals:. Alternative 1: take a job at a bank with a certain salary of $54,000 per annum. Alternative 2: take a job with a start-up company, get a base salary of $4,000 per annum a plus a bonus of $100,000 per annum a with probability 0.5 (otherwise bonus = $0). Show that Elizabeth would prefer Alternative 1 over Alternative 2 based on expected utility calculations.

Accepted Answer

The answer of Assume, Elizabeth's utility function is: U(W) =...

Question 8

Suppose your current wealth (W) is $8000 and you obey the principles of expected utility theory. Suppose you are offered a gamble where you can win $5000 with one-half chance but you can lose $5000 with one half-chance. Suppose your utility function is defined as U(W) = W^0.5. (The square root of your wealth). For you the risk premium of this is (approx.):

Accepted Answer

A)   878.
B)   7119.98
C)   8,000.
D)   89.44.

Question 9

Todd has $1000. He is given a choice of flipping a coin, heads wins $1000 while tails loses $500. Todd refuses to accept the gamble. A possible explanation is that:

Accepted Answer

A)   Todd is loss averse; so he prefers to avoid the gamble since his expected utility will be negative even though the expected value of the gamble is positive.
B)   Todd is risk neutral; so he prefers to avoid the gamble even though both the expected utility and the expected value of the gamble are positive.
C)   Todd is risk neutral; so he prefers to avoid the gamble since both the expected utility and the expected value of the gamble are negative.
D)   Todd is loss averse; so he prefers to avoid the gamble even though both the expected utility and the expected value of the gamble are positive.

Question 10

Jim Holtzhauer is playing the tables at Vegas. He currently has $10,000, which I will denote as 10K in order to keep things simple. He is looking at a bet where with ½ chance he can win 6K while with ½ chance he will lose 2K. Jim's utility of wealth function is given by U(W) = (W)^2. (U(W) is equal to the W Squared). Should Jim accept this gamble? If yes, why? If not, then why not? Does Jim have a certainty equivalent in this case? If yes, then what is this amount? Briefly explain whether this will imply Jim actually giving up money or Jim having to be given extra money in order to forego the gamble.

Accepted Answer

The answer of Jim Holtzhauer is playing the tables at...

Question 11

The risk premium of a gamble is defined as:

Accepted Answer

A)   The difference between the expected value of the gamble and the Certainty Equivalent; the amount you are willing to forego to avoid the gamble.
B)   The amount of money that makes an individual indifferent between receiving that amount for certain and taking on the gamble.
C)   The difference between the expected value of the gamble and the expected utility of the game.
D)   The initial endowment you started with prior to being faced with the gamble.

Question 12

For the Value Function in Prospect Theory, the magnitude of value increase from a gain of a particular size is smaller than the magnitude of the value decrease from an equivalent loss. Draw a neat diagram with the Value Function and explain what this means.

Accepted Answer

The answer of For the Value Function in Prospect Theory,...

Question 13

Respondents are given the following choices:
1) Choose between Gamble A: Win $4000 with probability 0.8 or Gamble B: Win $3000 for sure.
2) Choose between Gamble C: Lose $4000 with probability 0.8 or Gamble D: Lose $3000 for sure.
80% of respondents choose Gamble B over Gamble A; i.e. they prefer to win $3000 for sure over $3200 in expectation. But 92% of those same respondents chose Gamble C over Gamble D; i.e., they prefer to lose $3200 in expectation than lose $3000 for sure.
A potential explanation of this pattern of choices is that:

Accepted Answer

A)   People are risk seeking in losses but risk averse in gains.
B)   People are risk seeking in gains but risk averse in losses.
C)   People are risk neutral in losses but risk averse in gains.
D)   People evaluate gambles from a reference point and here the reference point is not clear, leading to inconsistent choices.

Question 14

Assume, Elizabeth's utility function is: U(W) = W^0.5 and she operates under the tenets of expected utility theory. She is considering two job proposals:. Alternative 1: take a job at a bank with a certain salary of $54,000 per annum. Alternative 2: take a job with a start-up company, get a base salary of $4,000 per annum a plus a bonus of $100,000 per annum a with probability 0.5 (otherwise bonus = $0).

Accepted Answer

A)   Elizabeth should choose Alternative 1 over Alternative 2 since the former yields expected utility of 232.4 while the latter yields expected utility of 192.9.
B)   Elizabeth should choose Alternative 2 over Alternative 1 since the former yields expected utility of 192.9 while the latter yields expected utility of 232.4.
C)   Elizabeth should choose Alternative 1 over Alternative 2 since the former yields expected utility of 89.4 while the latter yields expected utility of 86.44.
D)   Elizabeth should choose Alternative 2 over Alternative 1 since the former yields expected utility of 232.4 while the latter yields expected utility of 192.9.

Question 15

Ken Jennings has just been offered a job with a start-up company. The job pays $30,000 guaranteed per year. On top of that that there is a ½ probability that he can get a $50000 performance bonus making a total of $80,000. Ken, operates under the assumptions of expected utility theory and in general, has a strong preference for a job that pays a fixed amount per year. Ken's utility of wealth function is given by U(W) = $\surd$W. (U(W) is equal to the Square Root of W). Based on this information, you would conclude that:

Accepted Answer

A)   Ken will be willing to accept any job that pays approximately $52,000 per year or higher.
B)   Ken will be willing to accept any job that pays approximately $30,000 per year or higher.
C)   Ken will be willing to accept a job that pays $50,000 per year.
D)   Ken will be willing to accept a job that provides him with 200 utils of utility or less.

Question 16

Suppose your current wealth (W) is $8000 and you obey the principles of expected utility theory. Suppose you are offered a gamble where you can win $5000 with one-half chance but you can lose $5000 with one half-chance. Suppose your utility function is defined as U(W) = W^0.5. (The square root of your wealth). To you, the expected payoff from this gamble is:

Accepted Answer

A)   8,000.
B)   16,000.
C)   12,000.
D)   4,000

Question 17

The fact that people often ask for a much higher price for a good they possess than they are willing to pay to buy the same good is an example of:

Accepted Answer

A)   The endowment effect.
B)   Priming.
C)   Framing.
D)   The availability bias.

Question 18

Suppose I bought some Harvard mugs valued at $10.98. I gave half of the class a mug. These are the sellers. The other half do not have any mugs. They are the buyers. Neither side knows that true value of the mugs. Now supposed I asked the sellers to name a price at which they are willing to sell the mugs. At the same I asked the buyers to name a price at which they are willing to buy the mugs. It is likely that on average:

Accepted Answer

A)   The sellers will ask for a price higher than $10.98; the buyers will state a price less than $10.98. This is due to the endowment effect.
B)   The buyers will state a price higher than $10.98; the sellers will ask for a price less than $10.98. This is due to the endowment effect.
C)   The buying price and the selling price will be equal, since MLD students are all perfectly rational.
D)   The sellers will ask for a price higher than $10.98; the buyers will state a price less than $10.98. This is due to the sellers' over-confidence.

Question 19

Gamble A: Win $1000 with 0.50 probability or Gamble B: Win $500 for sure.
On the other hand, suppose you have won $2,000 on a game show and are then asked to choose between:
Gamble C: Lose $1,000 with 0.50 probability or Gamble D: Lose $500 for sure.
These two gambles are obviously identical in terms of final wealth states and probabilities. However, subjects are much more likely to choose the risk averse B and the risk seeking C. This suggests that participants:

Accepted Answer

A)   Are making their decisions over changes in wealth and are anchoring their choices on the basis of an initial reference point, rather than the final asset positions and wealth levels.
B)   Underweight the 0.5 probability after they win $1000 but overweight that same probability after they win $2000.
C)   Behave in accordance with expected utility theory since Gambles A and C yield higher expected value compared to Gambles B and D respectively.
D)   Overweight the 0.5 probability after they win $1000 but underweight that same probability after they win $2000.

Question 20