You participate in a coin-toss gamble with a weighted coin. The coin has a 70% chance of landing heads and a 30% chance of landing tails. If the coin lands heads, you receive $1000; if lands tails, you lose $2000. Your initial level of wealth is $3000 and your utility of wealth function can be modeled using the function U(wealth) = In(wealth).
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- Leo owns one share of Anteras, a semiconductor chip company which may have to recall millions of chips. The stock currently trades at $100/share. Leo believes the probability that they have to recall the chips is 50%. If the chips have to be recalled, the stock price will be cut in half, but otherwise it will remain $100. The expected value of Leo's share is ______ Assume Leo has the utility function, U(X)=√X. The minimum price Leo would accept to sell his share is _______ Leo's risk premium is ________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.Clancy has difficulty finding parking in his neighborhood and, thus, is considering the gamble of illegally parking on the sidewalk because of the opportunity cost of the time he spends searching for parking. On any given day, Clancy knows he may or may not get a ticket, but he also expects that if he were to do it every day, the average amount he would pay for parking tickets should converge to the expected value. If the expected value is positive, then in the long run, it will be optimal for him to park on the sidewalk and occasionally pay the tickets in exchange for the benefits of not searching for parking. Suppose that Clancy knows that the fine for parking this way is $100, and his opportunity cost (OC) of searching for parking is $20 per day. That is, if he parks on the sidewalk and does not get a ticket, he gets a positive payoff worth $20; if he does get a ticket, he ends up with a payoff of
- 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?Let U(x)= x^(beta/2) denote an agent's utility function, where Beta > 0 is a parameter that defines the agent's attitude towards risk. Consider a gamble that pays a prize X = 10 with probability 0.2, a price X = 50 with probability 0.4 and a price X = 100 with probability 0.4. Compute the agentís expected utility for such gamble and find the value of Beta such that the agentis risk neutral? Suppose B= 1, what is the certainty equivalent of the gamble described above? What is the Arrow-Pratt measure of absolute risk aversion?Consider a game where there is a $2,520 prize if a player correctly guesses the outcome of a fair 7-sided die roll.Cindy will only play this game if there is a nonnegative expected value, even with the risk of losing the payment amount.What is the most Cindy would be willing to pay?
- When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .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…Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R 5 250: 2$200, 2$100, $0, $100, $200, $300, $400, $500
- BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form. Form Type Mix of Forms Form Cost A 0.5 $3.00 B 0.5 $1.00 The expected cost of digitizing a form is . Suppose the client and BPO agree to a deal, whereby the client pays BPO to digitize forms. The price of each form processed is equal to the expected cost of the form that you calculated in the previous part of the problem. Suppose that after the agreement, the client sends only forms of type A. The expected digitization cost per form of the forms sent by the client is . This leads to an expected loss of per form for BPO. (Hint: Do not round your answers. Enter the loss as a positive number.)Consider the following game 1\2 Y Z A 10,2 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (1/3,2/3) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, Player 2 should respond by playing ____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.