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 10MC
To determine
Bid strategy
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Explain 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?)
Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a
premium. Jacob’s utility function for wealth is given by U(w) = In (w).
(A) What is the maximum
amount Jacob is willing to pay for this insurance? Show work and explain.
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.
Chapter 18 Solutions
Managerial Economics: A Problem Solving Approach
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- 10 Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.arrow_forwardSay 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.arrow_forwardChoice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work. (b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? can you help me for par (b) plase?arrow_forward
- Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? i need help with question B please.arrow_forwardSuppose 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…arrow_forwardRoger's utility/u as a function of wealth/w is u = { ln w, w < 1600 w1/2, w >= 1600 Roger has $1000 and 3 options. 1. spend $400 to enter the game with probabilities of winning or losing: Win/(Lose) (500) 0 1000 3000 P(Win/(Lose)) 0.2 0.1 0.6 0.1 a. Show with workings which option roger would choose.arrow_forward
- Anna is risk averse and has a utility function of the form u(w) pocket she has €9 and a lottery ticket worth €40 with a probability of 50% and nothing otherwise. She can sell this lottery ticket to Ben who is risk neutral and has €30 in his pocket. Find the range of prices that would make such a transaction possiblearrow_forwardReal Options & Game Theory Consider a stock that is priced at $200 today and a call option on that stock that gives you the right but not the obligation to buy the stock at $225 in one year’s time. There are only two scenarios: either an upside, on which the price rises to $300 or a downside that leads to a drop of $100. The risk free interest rate (rf) is 8%. What is the value of this option?arrow_forward2.Using the following table, perform ALL FIVE of the techniques for Decision Making under Uncertainty: Maximax, Maximin, Hurwicz Realism (α = 0.7), LaPlace and Minimax Regret. You must show your work. PROFIT ($) STRONG MARKET FAIR MARKET POOR MARKET Large facility 550,000 110,000 -310,000 Medium-sized facility 300,00 129,000 -100,000 Small facility 200,000 100,000 -32,000 No facility 0 0 0arrow_forward
- David 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_forwardSee 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_forwardWhy it is unwise to bid less than your valuation of the good in a sealed bid second-price auction. In the first price sealed bid auction, a player gets a positive payoff by doing bid shading. Explain the tradeoff between biding lower than the value of the object and biding very close to value of the object.arrow_forward
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