Question 1

Next suppose your utility function for value is U = 100(money).Are you risk averse, a risk lover, or risk neutral.

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Question 2

One thousand tickets are sold at $1 each for a color television valued at $350.What is the expected value of the gain if a person purchases one ticket?

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Question 3

Faced with the gamble: heads you win $100; tails you lose $50, we would predict that a risk-neutral person would

Accepted Answer

A risk-neutral person is not affected by the risk involved in the decision, but is only concerned with the potential payout. In this scenario, the expected value of the gamble is positive, as ($0.5 * $100) - ($0.5 * $50) = $25. As such, a risk-neutral person would take the gamble, as the potential gain outweighs the potential loss.

Question 4

Consider John, who purchases an insurance policy on a racquetball racket that he has acquired.He then proceeds to hit his racket against the wall every time he losses a point .This is an example of

Accepted Answer

John's behavior of hitting his racket against the wall is a deliberate action that increases the likelihood of damage to the racket, and he may not bear the full cost of repairing or replacing the racket due to the insurance policy. This demonstrates a moral hazard problem, where the presence of insurance alters John's behavior, leading to increased risk-taking.

Question 5

(Appendix) The winner in an auction bidding process will

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Question 6

Your utility function is given by U = M^1/2.What is the expected utility of the following coin toss: heads you win $81, tails you win $100?

Accepted Answer

The expected utility is calculated by taking the average of the utility of each outcome. For heads, the utility is √81 = 9, and for tails, the utility is √100 = 10. The expected utility is (9 + 10) / 2 = 9.5.

Question 7

For a large group of individuals, the proportion of people who will have accidents is

Accepted Answer

For a large group of individuals, statistical methods allow for the prediction of accidents with a high degree of accuracy. This predictability is based on historical data and probability theories that can forecast the likelihood of accidents within large populations.

Question 8

What is the maximum you would pay security to check in your bike?

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Question 9

Your bike is worth $100 and if you park it outside at school there is a 25% chance that it will be stolen.Your utility function for money is U = (money)².Are you a risk taker?

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Question 10

Megan is trying to decide whether to buy house insurance for her home in Miami.Her house is worth $200,000 and analysts have determined that the average loss from a Hurricane could be $45,000.They have also determined there is a 50 percent chance that she will face a hurricane.Suppose Megan is a risk averse person with a utility-of-income function such as the one given above.If the policy costs $22,500, Megan will

Accepted Answer

Megan is risk-averse, which means she prefers a certain outcome over an uncertain one. In this case, the risk of facing a hurricane and incurring a loss of $45,000 is uncertain, and Megan would prefer to avoid it. The expected value of her loss is (0.5 x $45,000) = $22,500. The cost of insurance is also $22,500. Therefore, buying insurance would give her a certain outcome of paying $22,500, which she may prefer over the uncertain outcome of either no loss or a loss of $45,000. Hence, Megan should buy the insurance.

Question 11

Your utility function is given by U = M².You are

Accepted Answer

A utility function U = M^2 indicates a risk seeker because the utility increases at an increasing rate as wealth (M) increases, suggesting a preference for riskier options with potentially higher returns.

Question 12

(Appendix) If the cost of search is $3, and wages are uniformly distributed between $20 and $50, what is the smallest wage you should accept if you are risk neutral?

Accepted Answer

The smallest wage you should accept, often referred to as the reservation wage, can be calculated using the formula for the expected wage (E[W]) minus the cost of search. Given that wages are uniformly distributed between $20 and $50, the expected wage is the average of these two values, which is $35. The cost of search is $3, so the reservation wage is $35 - $3 = $32. However, none of the provided options exactly match this calculation. The closest option to the correct theoretical answer is $36.58 (A), suggesting a possible miscalculation in the question setup or a misunderstanding of the provided options. In practice, the correct approach involves setting the expected gain from searching equal to the cost of search, and solving for the reservation wage in the context of the uniform distribution's properties.

Question 13

Your utility function is given by U = M^1/2.You have a choice: take $100 in cash or flip a coin.If you flip a coin, the outcomes are as follows: heads, you win $225; tails, you win $49.You will

Accepted Answer

To make the decision, we need to compare the expected utility of each option. If we choose the $100 in cash, our utility would be:

U(cash) = M*S1*U1*P1^1/2*S1*S1*P0 = M*1*U1*1*1*1 = M*U1

If we choose to take the gamble, our expected utility would be:

U(gamble) = 1/2*(M*S1*U1*(225/100)^1/2*S1*S1*P0) + 1/2*(M*S1*U1*(49/100)^1/2*S1*S1*P0)
= 1/2*(M*U1*(15/10)*(1/2)) + 1/2*(M*U1*(7/10)*(1/2))
= M*U1*0.55

Since the expected utility of the gamble (0.55*M*U1) is greater than the utility of taking the cash (M*U1), we should choose to take the gamble.

Question 14

What is the expected value of your bike in the scenario described in the question above?

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Question 15

(Appendix) If you have an offer of $10/hour and the relevant range of offers is $5/hour to $15/hour with the offers proportionately distributed across the range, what is your expected gain from engaging in a search for another offer?

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Question 16

You are given the following gamble: behind one door is $500; behind another is $100; behind another is $0.What is the expected value of the gamble?

Accepted Answer

There are three possible outcomes, each with a probability of $\frac13$. Therefore, the expected value is:
$$\frac13(\$500) + \frac13(\$100) + \frac13(\$0) = \$200$$
The best choice is to pick the door with the highest expected value, which is $\$500$. However, since we don't know which door that is, we cannot make the best choice with certainty.

Question 17

When a trading opportunity is presented to a heterogeneous group of potential traders, those who accept it will be often:

Accepted Answer

This is known as adverse selection or the "lemons problem." Those who accept the trading opportunity are more likely to have private information or inside knowledge that makes the investment more attractive to them, and less attractive to others. As a result, they are more likely to be worse-off on average than those who do not accept the opportunity.

Question 18

You are thinking of buying a new computer.Before purchasing a particular model, you have decided to gather some information about all the computer models available to you.The amount of information you collect should only be dependent on:

Accepted Answer

It is important to consider both the cost of the information and how much you want the computer in order to make an informed decision. Collecting too little information may result in regretting the purchase later, while collecting too much information may cost more than necessary. Therefore, the best choice is to balance the cost of the information with the importance of the purchase.

Question 19

Campus security has a bike check in that will guard your bike for $15 so there will be no risk of loss.Do you take the campus security deal?

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Question 20

If the slope of a person's utility function for different money prizes is linear, the person

Accepted Answer

A linear utility function indicates constant marginal utility of money, meaning the person is indifferent to risk.

Quiz 6: The Economics of Information and Choice Under Uncertainty