If only lottery A is available at price 45, should you buy it? If only lottery B is available at price 34, should you buy it? (b) If both lottery A and lottery B are available at prices 45 and 34, respectively, should you buy the lotteries?
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- A decision maker has a utility function for monetary gains x given by U(x) = (x + 10,000)1/2. (a) Show that the person is indifferent between the status quo and L: With probability 1/3, he or she gains $80,000 With probability 2/3, he or she loses $10,000 (b) Suppose that this person has a painting. If there is a 10% chance that the painting valued at $10,000 will be stolen during the next year, what is the maximum amount (per year) that he/she would be willing to pay for insurance covering the loss of the painting? • What is certainty equivalent? • What is risk premium? (c) Is this person risk-averse, risk-neutral, or risk-taker? Why?Ann is a risk averse individual with the utility function u(w) = w1/2. Her current wealth is $300 and with the probability 0.25 she will incur a huge loss of D = 240, but with the probability 0.75 she will incur no loss. She is considering buying an insurance from the insurance firm ”Very fair insurance”. (a) The ”Very fair insurance” firm sells the actuarially fair insurance to its customers. What premium would they charge Ann per dollar of insurance?Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
- Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γ E[I], where γ >1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1. [Hint: draw a coordinate plane with p on the x-axis and M on the y-axis.] Based on this graph, under what conditions is she least likely to buy the subsidized insurance?A consumer is given the chance to buy a baseball card for $1, but hedeclines the trade. If the consumer is now given the baseball card, willhe be willing to sell it for $1? Standard consumer theory suggests yes, butbehavioral economists have found that “ownership” tends to increase thevalue of goods to consumers. That is, the consumer may hold out for someamount more than $1 (for example, $1.20) when selling the card, eventhough he was willing to pay only some amount less than $1 (for example,$0.88) when buying it. Behavioral economists call this phenomenon the“endowment effect.” John List investigated the endowment effect in a randomized experiment involving sports memorabilia traders at a sports-card show. Traders were randomly given one of two sports collectibles, say good A or good B, that had approximately equal market value.1 Those receiving good A were then given the option of trading good A for good B with the experimenter; those receiving good B were given the option of…Ana’s preferences are consistent with expected utility. Denote by u(x) her utility function for a monetary outcome £x, and suppose that she is strictly risk-averse. Ana currently faces the monetary lottery which pays: £A with probability pA; £B with probability pB; and £C with probability pC. Now suppose that Ana is made the following o§er. For each realization of the original lottery, another lottery will be executed according to which she wins an additional poundwith probability 1/2 and loses a pound with probability 1/2. Describe the lottery that Ana faces if she accepts the o§er by describing the new payo§s and probabilities over these payo§s. (b) Show that she rejects the o§er and explain why.
- To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3,400, and the commission for each new account opened is $4,900. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account. Determine the equation for computing Gustin's profit per seminar, given static values of the relevant parameters. Profit =(New accounts opened x _______)-_________ Construct a simulation model to analyze the profitability of Gustin's seminars. Would you recommend that Gustin continue running the seminars? (Use at least 1,000 trials. Round your answer to two decimal places.) What is the minimum number of attendees (in a multiple of five, i.e., 25, 30, 35, …) that Gustin needs before a seminar's average profit is greater than zero? =______ attendeesA decision maker has a utility function for monetarygains x given by u(x) (x 10,000)1/2. a Show that the person is indifferent between the sta-tus quo and L: With probability 13, he or she gains $80,000 L: With probability 23, he or she loses $10,000b If there is a 10% chance that a painting valued at$10,000 will be stolen during the next year, what is themost (per year) that the decision maker would be willingto pay for insurance covering the loss of the painting?A store manager observes that the morale of employees in her supermarket is low. She thinks that if their working conditions are improved, pay scales rose, and the vacation benefits made more attractive, the morale will be boosted. She doubts, however, if an increase in pay scales would raise the morale of all employees. Her conjecture is that those who have supplemental incomes will just not be “turned on” by higher pay, and only those without side incomes will be happy with increased pay, with a resultant boost in morale Based on the scenario presented, answer the following questions: A) Identify the Independent, Dependent, Moderating, and Mediating Variables. Also provide justification for your choice. B) Create a schematic diagram (i.e., conceptual framework) that depicts the relationships among the variables. C) Based on the above conceptual framework develops at least four alternate hypotheses.
- Suppose that speeding imposes externalities on other people resulting in a social cost of $50. A town is considering hiring an extra police officer to give out speeding tickets. If we want to maximize social welfare (absent enforcement costs), which of the following statements are true? (Assume risk neutral drivers.) a) If the probability of detection with the extra police officer is 10%, then a speeding ticket should cost $55. b) If the probability of detection with the extra police officer is 10%, then a speeding ticket should cost $500. c) If the probability of detection with the extra police officer is 100%, then no one will speed. d) If the probability of detection with the extra police officer is 90%, then a speeding ticket should cost $59 e) None of the aboveSuppose there are two people, Selma and Burak, who must split a fixed income of 200. The marginal utilities of income for Selma and Burak are as follows: MUs = 600- 2*Is MUB = 600- 4*IB where IS and IB are incomes of Selma and Burak respectively. What is optimal distribution of income if social welfare function is additive? Draw the MUof Selma and Burak in the Edgeworth box and show part (a). What is the optimal distribution if society values only the utility of Selma? What is the optimal distribution if society values only the utility of Burak? This example refers to ……… ………. rationale for income redistribution and it is Pareto ………….V1. Suppose Sally has a choice to undertake a risky job for a salary of $69828. She could choose to take a safe job for a salary of $62841. She decided to take the risky job. Assuming Sally has a 1 in 601 chance of dying at the risky job then using the trade-off method, she values her life at:
