Consider a lottery with three possible outcomes: $120 with probability 0.3, $80 with probability 0.2 and $50 with probability 0.5. What is the expected value of the lottery? What is its variance? (Please submit answers as integers, for example, 189 or 32) the expected value of the lottery is ———— the variance is —

Consider a lottery with three possible outcomes: $120 with probability 0.3, $80 with probability 0.2 and $50 with probability 0.5. What is the expected value of the lottery? What is its variance? (Please submit answers as integers, for example, 189 or 32) the expected value of the lottery is ———— the variance is —

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 9MC

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Consider an individual who maximizes his expected utility with the following utility function: U(x) = logX He is faced with the lottery with the following probabilities and payoffs Probability Money 0.4 30 0.5 100 0.1 50 a. Find his expected utility b. Calculate the Certainty Equivalent c. Find the amount that the individual will be willing to pay in order to avoid the lottery (That is, the risk premium)
For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving. a. A manager prefers a 20 percent chance of receiving $1,400 and an 80 percent chance of receiving $500 to receiving $680 for sure. b. A shareholder prefers receiving $920 with certainty to an 80 percent chance of receiving $1,100 and a 20 percent chance of receiving $200. c. A consumer is indifferent between receiving $1,360 for sure and a lottery that pays $2,000 with a 60 percent probability and $400 with a 40 percent probability.
For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving.a) A manager prefers a 10 percent chance of receiving $1,000 and a 90 percent chance of receiving $100 to receiving $190 for sure.b) A shareholder prefers receiving $775 with certainty to a 75 percent chance of receiving $1,000 and a 25 percent chance of receiving $100.c) A consumer is indifferent between receiving $550 for sure and a lottery that pays $1,000 half of the time and $100 half of the time.
Company ABC holds an auction. Five bidders were invited. Company ABC estimates that each bidder has a value of either 15 or 25 for the item, and the probabilities attach to each value is 50%. What is the expected price? What is the price if three of the five bidders collude?
A risk-averse manager is considering two projects. The first project involves expanding the market for bologna; the second involves expanding the market for caviar. There is a 10 percent chance of a recession and a 90 percent chance of an economic boom. During a boom, the bologna project will lose $10,000, whereas the caviar project will earn $20,000. During a recession, the bologna project will earn $12,000 and the caviar project will lose $8,000. If the alternative is earning $3,000 on a safe asset (say, a Treasury bill), what should the manager do? Why?
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You are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table. Project Boom (50%) Recession (50%) A $ 20 −$ 10 B −$ 10 $ 20 C $ 30 −$ 30 D $ 50 −$ 50 The variance in the returns of project D is Multiple Choice 1,600. 225. 900. 0.
Solve the following problem using an excel spreadsheet. A tobacco company isinterested in hiring a salesperson to promote smoking cigarettes in nightclubs. The position pays a flat salary of $50,000, regardless of sales levels. The firm has two applicants, Predictable Patty and Risky Ricky. Predictable Patty can produce with 100% certainty $100,000 a year in sales. Risky Ricky, on the other hand, can produce $300,000 with probability of 50%. But if he turns out to spend his time drinking and dancing in the nightclubs instead of making sales, he could actually cost the firm -$100,000 per year.a) During their first year on the job, what are the expected sales of Patty and Ricky? What are the firm’s expected profits on each worker?b) Now assume both workers are currently 25, and they will work until the retirement age of 65. The firm has the option to fire its new employee after one year based on sales, but can only hire one employee. Assume that it takes only one year to discover whether…
Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.
The following payoff table provides profits based on various posible decision alternativesand various levels of demand at Kmart Print Shop. Alternatives Low High Alternative 1 10,000 30,000 Alternative 2 5,000 40,000 Alternative 3 -2,000 50,000 The probability of low demand is 0.4, whereas the probability of high demand is 0.6.What is the highest possible expected monetary value?
You have a 50 percent chance of making $0, a 40 percent chance of making $100, and a 10 percent chance of losing $100. Calculate the expected value and variance of the payoff.
You need to hire some new employees to staff your startup venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them: Employee Value Probability $65,000 0.25 $82,000 0.25 $99,000 0.25 $116,000 0.25 The expected value of hiring one employee is . Suppose you set the salary of the position equal to the expected value of an employee. Assume that employees will not work for a salary below their employee value. The expected value of an employee who would apply for the position, at this salary, is . Given this adverse selection, your most reasonable salary offer (that ensures you do not lose money) is .