Consider a risk-neutral agent who maximizes expected utility of wealth facing a lottery with a "bad" (wealth remains the same) and a "good" (wealth increases by a small amount) outcome (both with non-zero probabilities). For this agent, O the certainty equivalent will be zero, but the risk premium will be greater than zero. O the certainty equivalent will be greater than zero, but the risk premium will be zero. O the certainty equivalent will be greater than zero, but the risk premium will be less than zero. O the certainty equivalent will be less than zero, but the risk premium will be greater than zero, O the certainty equivalent and the risk premium will both be zero. O there is not enough information to make statements about the certainty equivalent and the risk premium.
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- 1. A woman with current wealth X has the opportunity to bet an amount on the o ccurrence of an event that she knows will occur with probability P. If she wager s W, she will received 2W, if the event occur and if it does not. Assume that t he Bernoulli utility function takes the form u(x) = -e-TX with r> 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?1. A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and o if it does not. Assume that the Bernoulli utility function takes the form u(x) = -e-rx with r>0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?
- 2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?Your friend is contemplating buying a local restaurant. He has assessed the lifetime profits, including resale, to be $11 million with 20% chance, $6 million with 60% chance or $3 million with 20% chance. Knowing the most your friend would pay for the restaurant is $6.4 million, what can you infer about the situation? O A. The expected payoff of the restaurant is $6.333 million, the risk-discount being offered by your friend is $77.000 and your friend is risk averse with respect to this purchase. O B. The expected payoff of the restaurant is $6.4 million, the risk-premium being required by your friend $0 and your friend is risk neutral with respect to this purchase. o C. The expected payoff of the restaurant is $6.4 million, the risk-premium being required by your friend $200,000 and your friend is risk seeking with respect to this purchase. O D. The expected payoff of the restaurant is $6.333 million, the risk-premium being required by your friend is $333,000 and your friend is risk…Anne has $138.40 and is thinking about buying a lottery ticket. The lottery pays $4.00 with probability 0.20 and $172.00 with probability 0.80. To buy the ticket, Anne would need to spend all her money. Suppose we observe Anne buying the ticket. What can we infer about Anne? Choose one: O A. We cannot infer that Anne is risk neutral. O B. We can infer that Anne is not risk averse. O C. We cannot infer anything. O D. We can infer that Anne is risk averse.
- Consider two uncertain outcomes W₁ and W₂, each of which has a 50% probability of occurring. The household's expected utility function is given as: U(M)=10W-W². If W₁-2 and W₂=4, what are the expected utility of wealth and the utility associated with the expected wealth? O The expected utility of wealth is 20, while the utility associated with the expected wealth is 21. O The expected utility of wealth is 21, while the utility associated with the expected wealth is 20. O The expected utility of wealth is 24, while the utility associated with the expected wealth is 16. O The expected utility of wealth is 16, while the utility associated with the expected wealth is 24. O Both the expected utility of wealth and the utility associated with the expected wealth are 24. O No answer. AJin's Utility Function Wealth Utility (Dollars) 60,000 4,000 61,000 4,110 62,000 4,209 63,000 4,288 Refer to Table 27-1. If Jin's current wealth is $61,000, then O his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is risk averse. his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is risk averse.You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
- Charles is participating in an experiment. His payoff in the experiment is tied to his effort e doing a mundane task. There is also some risk involved by design-there is a chance p that Charles is going to get a fixed payment L regardless of his effort. Charles' payoff is thus: with probability p w.e with probability 1- p Charles has to pay a cost C, which increases with his effort. First, let us assume that Charles' utility is the expected payoff net of this cost: U(e) = pL + (1 – p)we – c(e) Derive the first order condition with respect to e. b. How doesp affect Charles' effort e? c. How does L affect e?Your utility function is U = w, where W is your wealth. Your current wealth is $800. There is a 25% chance that you will suffer a loss of $600. You are: O Risk Averse O Risk seeking O Risk neutral O Risk encumberedSuppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…