Q1 Market-clearing Prices Consider a standard position auction. There are two positions: Top (T) and Bottom (B). Position T receives ¤7 = 150 clicks per day and position B receives rB = 50 clicks per day. There are four bidders (B1-B4) with the following dollar values per click: v1 = 8, vz = 6, v3 = 4, v4 = 2. %3D (a) Find the efficient assignment. (b) Find the lowest per click market-clearing prices. (c) Find the highest per click market-clearing prices. (d) Fully specify and draw the complete set of ALL per click market-clearing prices.
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- ONLY SOLVE D An investor with a total wealth of $100 is faced with the following opportunities. First, he may invest $100 now and receive $144 if there are good times, but receive $64 if there are bad times. The investor estimates that good times happen with 50% probability.He can also buy an investor newsletter whether good times or bad times will occur. (a) Draw the decision tree that illustrates the options available to the investor and the payoffs to the different options. Define P as the price of the newsletter. (b) If the investor is risk-neutral with U(M) = M, where M is income, how much would he be willing to pay for the subscription to the newsletter? (c) If the investor is risk-averse with utility U(M) = M0.5, where M is income, how much would this investor be willing to pay for the subscription to the newsletter? (d) Suppose that the owner of the newsletter estimates that there are 75 risk-averse investors like those of part (c) and 25 investors like those of part(b). If…4.25 The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): State of Nature Low Demand Medium Demand High Demand Decision Alternative s1 s2 s3 Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. Use a decision tree to recommend a decision.Recommended decision: Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.EVPI: $1. Individual Problems 18-1 You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125 3 $88 $110 $88 0.125 4 $88 $110 $110 0.125 5 $110 $88 $88 0.125 6 $110 $88 $110 0.125 7 $110 $110 $88 0.125 8 $110 $110 $110 0.125 The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders…
- 1 . Individual Problems 17-2 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 $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. 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 . Given that this is , you 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 . (Hint: At what probability does playing the final round yield an expected value of zero?)There are N>=2 collectors who engage in the auction of an antique. The collectorshave a common valuation of the antique, denoted by v, which is known to all. Thecollectors make a simultaneous bid. Let pn denote the bid by collector n = 1,....,N. The one with the highest bid wins the antique. The winner receives payoff v-pi.The other(s) receive zero payoff. If more than one collectors make the same highestbid, then they have an equal chance of winning the item. Prove that: A) It is not a Nash Equilibrium (NE) if the highest bid is v and onlyone collector bids this price.(b) It is not a NE if the highest bid is less than v.(c) It is a NE that the highest bid is v and more than one collector bidsthis priceWhen 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 $_______. .
- onsider the game described by the ff table. what is thE best response for the column player if he/she knows that the row player will make the Y move?4.7 Hudson Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows: Demand Staffing Options High Medium Low Own staff 650 650 600 Outside vendor 900 600 300 Combination 800 650 500 If the demand probabilities are 0.2, 0.5, and 0.3, and the table below shows the total cost of the different options, construct a risk profile for the optimal decision in the table. Option Total Cost Own Staff 635 Outside Vendor 570 Combination 635A manager is deciding whether to build a small or a large facility. Much depends on the future demand that thefacility must serve, and demand may be small or large. The manager knows with certainty the payoffs that willresult under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values offuture revenues minus costs for each alternative in each event.What is the best choice if future demand will be low?
- Question 1 Consider a first-price sealed bid auction of a single object with two biddersj = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation isv1 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts.In the event of a tie, the object is awarded by a flip of a fair coin.(a) Find an equilibrium of this game.(b) Is the allocation of your answer to (a) efficient?1. Draw tree of the game clearly, handwritten is preferable.First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Ernie, Teresa, and Marilyn. First Fiddler's 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. First Fiddler's believes that these probabilities are in de pendent among buyers. If First Fiddler's sells the house by means of a second- bidder, sealed- bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.) The closest option is 448, 148. Please explain in details thank you.