Managerial Economics: A Problem Solving Approach
5th Edition
ISBN: 9781337106665
Author: Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher: Cengage Learning
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Chapter 18, Problem 8MC
To determine
Winner’s curse.
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Two parties, Juan and Ben, have been negotiating the purchase by Ben of Juan's car. Juan receives a new and higher bid for his car from Adriana. How might Adriana's bid change Juan and Ben's threat values?
The threat values are unchanged.
Juan now values the car at the price of Adriana's bid, her bid is his opportunity cost of selling the car to Ben, and that opportunity cost is Juan's new threat value.
Juan's new threat value is the product of the difference between Ben and Adriana's offers and the probability the car will be sold to Adriana.
Juan's threat value is unchanged, but Ben has to consider his new opportunity cost
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.
Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2.
In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid.
a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…
Chapter 18 Solutions
Managerial Economics: A Problem Solving Approach
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- See attachments for question context. Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.arrow_forwardText of the problem from 'An introduction to decision theory' by Martin Peterson: You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in which you win $200 with a probability of 1/4, $50 with a probability of 1/4, and $10 with a probability of 1/2. You also prefer a fifty-fifty chance of winning either $200 or $50 to receiving $100 for sure. Are your preferences consistent with von Neumann and Morgenstern’s axioms? The book proposes as solution 'No. Your preferences violate the independence axiom.' without proposing the steps to reach that solution and I don't know why it is correct.arrow_forwardDavid wants to auction a painting, and there are two potential buyers. The value for eachbuyer is either 0 or 10, each value equally likely. Suppose he offers to sell the object for $6, and the two buyers simultaneously accept or reject. If exactly one buyer accepts, the object sold to that person for $6. If both accept, the object is allocated randomly to the buyers, also for $6. If neither accepts, the object is allocated randomly to the bidders for $0. (a) Identify the type space and strategy space for each buyer. (b) Show that there is an equilibrium in which buyers with value 10 always accept. (c) Show that there is an equilibrium in which buyers with value 10 always reject.arrow_forward
- Consider a first-price, sealed-bid auction, and suppose there are only three feasible bids: A bidder can bid 1, 2, or 3. The payoff to a losing bidder is zero. The payoff to a winning bidder equals his valuation minus the price paid (which, by the rules of the auction, is his bid). What is private information to a bidder is how much the item is worth to him; hence, a bidder’s type is his valuation. Assume that there are only two valuations, which we’ll denote L and H, where H > 3 > L > 2. Assume also that each bidder has probability .75 of having a high valuation, H. The Bayesian game is then structured as follows: First, Nature chooses the two bidders’ valuations. Second, each bidder learns his valuation, but does not learn the valuation of the other bidder. Third, the two bidders simultaneously submit bids. A strategy for a bidder is a pair of actions: what to bid when he has a high valuation and what to bid when he has a low valuation. a. Derive the conditions on H and L…arrow_forward“While auctions are appealing in theory, the challenges of auction design in practice are insurmountable” discussarrow_forwardExplain why a player in a sealed-bid, second-price auction would never submit a bid that exceeds his or her true value of the object being sold. (Hint: What if all players submitted bids greater than their valuations of the object?)arrow_forward
- Give an example, real or imaginary, of a moral hazard problem. Again, your example must clearly point out: what information is private/asymmetric (is it an attribute or an action?) which party has the private information when does the information asymmetry arise (before or after the contract/transaction?) what is the likely outcome and in which way it can be inefficientarrow_forwardThe conventional wisdom for urban economic development is: “Don’t put all your eggs in one basket. Diversify the economy.” To explain the idea of diversification, consider old McDonald, who must carry a dozen eggs from the barn to the house. The ground between the barn and the house is slippery, so there is a 50 percent chance that McDonald will slip on a given trip and break all the eggs in his basket. Consider two strategies: a one-basket strategy (a single trip with all 12 eggs) and a two-basket strategy (two trips, with 6 eggs per trip). INDEPTH ANSWERS. Questions= (1.)List all of the possible outcomes under each of the strategies. Question (2.)What is the expected number of delivered (unbroken) eggs under each strategy ? Question (3.)What are the trade-offs between the two strategies? If you were McDonald, which strategy would you adopt? Question (4.)What are the lessons for economic development strategies?arrow_forward5. Individual Problems 18-5 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 Simone places a value of $65,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Simone simply bids $65,0002=$32,500$65,0002=$32,500 and wins the piece of art. The expected price paid by Simone, with no other bidders present, is . Suppose the owner of the artwork manages to recruit another bidder, Yakov, to the auction. Yakov is known to value the art piece at $52,000. The expected price paid by Simone, given the…arrow_forward
- In a sealed-bid, second-price auction with complete information, the winner is the bidder who submits the second-highest price, but pays the price submitted by the highest bidder. Do you agree? Explain.arrow_forwardConsider the following model about the auctions. We have two buyers each obtain a private signal about the value of good being auctioned. The signal can be either high (H) or low (L) with equal probability. If both obtain signal H, the good is worth 1; otherwise, it is worth 0.a. What is the expected value of the good1 to a buyer who sees signal L and to a buyer who sees signal H?b. Suppose buyers bid their expected value computed in part (a). Show that they earn negative profit conditional on observing signal H.arrow_forwardBPO 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.)arrow_forward
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