Prediction markets allow traders to bet on future events. One prediction market that is particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2.

Prediction markets allow traders to bet on future events. One prediction market that is particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.8P

See similar textbooks

Similar questions

Suppose a company is hiring graduates from Harvard and Yale and they want to hire people with very high predicted productivity. All they use to predict productivity is where they went to school and their GPA. There is no difference in average true ability between students at Harvard and Yale. However, while Yale GPAs are excellent predictors of performance at this company, Harvard GPAs are not. The company hires very few graduates and the cutoff for expected productivity is well above average. What will be true about the GPA cutoffs for the two schools? A. The cutoff for Harvard will be higher.B. The cutoff for Yale will be higher.C. The cutoffs will be the same.D. There is not enough information to answer this question.
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 $_______. .
Consider the following compound lottery, described in words: "The probability that the price of copper increases tomorrow is objectively determined to be 0.5. If it increases, then tomorrow I will flip a coin to determine a monetary payout that you will receive: if the flip is Heads, you win $100, while if it is Tails, you win $50. If it does not increase, then I will roll a 10-sided die (assume each side is equally likely to be rolled). If the die roll is a 4 or lower, you will win $100. If it is a 5, then you will win $200, and if it is a 6 or greater, you will win $50." Fill in the blanks below for the reduced lottery that corresponds to this compound lottery (write in decimals). R= ( , $50; , $100; , $200)
You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is [$ blank]. Given that this is positive [blank (positive/negative)], you should [blank (should/should not)] play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is [blank]. (Hint: At what probability does playing the final round yield an expected value of zero?)
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.)
We learned that we can use choice between a gamble over someone's best and worst outcomes and getting an outcome of interest (like getting pizza) for certain as a way to assign numeric values to utility (on a scale of 0 to 1). Using this method, if you are indifferent between the following: A gamble that has a 0.3 chance of your best possible outcome (and no lower chance), and a 0.7 chance of your worst possible outcome. Getting pizza for certain. it means that your utility for getting pizza is:
When real estate agents sell their own, rather than clients', houses, they leave the houses on the market for a longer time (10 days longer on average) and wind up with better prices. Suppose that real estate agents earn a commission equal to 3% of the sale value of each house that they help sell. Suppose a real estate agent has an offer on a house of $600,000. The agent can get a 4% higher offer with more effort and by leaving the house on the market for a few more weeks. If the agent sells the house now, she will earn a commission of . By keeping the house on the market and expending more effort to sell the house, the agent can earn a commission of . Thus, the agent gains for the extra effort and time of keeping the house on the market. Suppose a real estate agent has an offer on a house that she owns. The agent has a current offer of $600,000, but can get a 4% higher offer with more effort and by leaving the house on the market for a few more weeks. Assume that all of…
Joe's search costs are $5 per search. He wants to buy a smart watch for his wife for Christmas, and the lowest price he's found so far is $300. Joe thinks 80 percent of the stores charge $300 for smart watches and 20 percent charge $200. Joe's optimal decision is to Multiple Choice continue to search for a lower price since the expected benefit of an additional search is $20, which exceeds his per-unit search costs. continue to search for a lower price since the expected benefit of an additional search is $80, which exceeds his per-unit search costs. stop searching and purchase a video player for $300. continue to search for a lower price since the expected benefit of an additional search is $100, which exceeds his per-unit search costs.
Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $350,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $400,000, there is a 0.5 chance you will be able to sell the machine. If you commit to a price of $450,000, there is a 0.2 chance you will be able to sell the machine. If you commit to a price of $500,000, there is a 0.15 chance you will be able to sell the machine. These probabilities are summarized in the following table. For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the machine to your company in the event that you are not be able to sell the machine.) Posted Price Probability of Sale Expected Value ($) ($) $500,000…
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 if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…
Youngstown-Warren Regional Airport (YNG) has had a difficult time securing passenger service from a commercial airline. a.) A few years ago, the Port Authority offered an incentive to United with guaranteed revenue equal to approximately $1.5 million, but United declined saying it was not sufficient. Suppose United anticipated that it would cost $1 million to offer flights from Youngstown, so with a guaranteed revenue of $1.5 million, their anticipated profit would equal $500,000. Given that they still chose to decline offering service from YNG, what do you know must be true? Put this in terms of implicit costs and economic profit. b.) In 2019, YNG’s only commercial carrier, Allegiant Air stopped offering service from YNG, despite the fact that it was known to be profitable. Allegiant Air’s service from YNG was known to be profitable. Why would Allegiant Air pull service from YNG even if it had been their service from YNG had been generating a profit? Note, Allegiant started…
Say that you are bidding in a sealed-bid auction and that you really want the item being auctioned. Winning it would be worth $500 to you. Say you expect the next-highest bidder to bid $300.a. In a standard “highest-bid” auction, what bid would a rational person make? The rational choice is to bid $500 since that is what the item is worth to you. The rational choice is to bid a little bit more than $300 because that is the expected next-highest bid. The rational choice is to bid just under $500 so that you have a higher chance of winning the auction and would still have a net benefit. The rational choice is to bid over $500 to guarantee that you win the item. b. In a Vickrey auction, what bid would he make? The rational choice is to bid slightly more than $500. The rational choice is to bid $500. The rational choice is to bid slightly less than $500. The rational choice is to bid slightly more than $300.