ou 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.
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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.
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- Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?Obi-Wan is considering whether to buy a lightsaber. With probability 0.50 he will value the lightsaber at $4,000, and with probability 0.50 he will value it at $1,000. If new lightsabers sell for $2,500, then buying a new lightsaber is a: Multiple Choice fair gamble. better-than-fair gamble. less-than-fair gamble. less-than-fair gamble if Obi-Wan risk neutral.Consider a lottery with three possible outcomes: $100 will be received with probability .1, $50 with probability .2, and $10 with probability .7. What is the expected value of the lottery? What is the variance of the outcomes of the lottery? What would a risk-neutral person pay to play the lottery?
- 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.Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000. Portsmouth Bank believes that these probabilities are independent among buyers. If Portsmouth Bank sells the house by means of a second- bidder, sealed- bid auction (Vicktey auction), what will be the bank's expected revenue from the sale?You take a position with a large real estate development company as your first job after graduation. Your first big assignment is to sell an office building – you have been informed the company’s cost into the building (and the bottom line price it is willing to accept) is $400,000. You have identified a likely buyer and you assess that his top price is either $500,000 with a probability of .3, $600,000 with a probability of .5, or $1,000,000 with a probability of .2. You have to commit to a posted price – what price will maximize your profitability?
- The table below shows that a sales agent can work with either low, or high amount of effort. Low effort generates$30,000, $60,000 or $100,000 profit (with probability given below), while high effort generates 60,000; 100,000 or 150, 000 (with probability given below) depending on some random factors. Bad luck (P=0.3) Medium luck (P=0.3) Good luck (P=0.4) Low effort (a=0) $30,000 $60,000 $100,000 High effort (a=1) $60,000 $100,000 $150,000 The cost of low effort is 0 and the cost of high effort is $10,000 (Formally, c=$10,000a). The net wage is wage minus cost of effort and the net profit is total profit minus wage. Suppose the firm offers the repair person a fixed wage of 13,000, what will be the net wage of the repair person and the net profit of the owner? Suppose now the owner offers the repair person the following bonus arrangement What will be the net wage of the repair person? What will be the net profit of the owner? Specify…Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.As risk aversion increases, which direction does the certainty equivalent wealth move, holding the bet fixed?
- Calculate the risk premium of John when he faces the risky prospect X = {1, 4, 9, 16; 0.2, 0.4, 0.4, 0.0} . His utility function is u ( x ) = x , where x is wealth. (Use two decimals)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)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…
