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 secondhandmarket lead you to believe that if you commit to a price of $400,000, there is a 0.4 chance you will be able to sell the machine. If you commit to a price of $450,000, there is a 0.25 chance you will be able to sell the machine. If you commit to a price of $500,000, there is a 0.1 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.)

John wants to buy a used car. He knows that there are two types of car in the market, plums and lemons. Lemons are worse quality cars and are more likely to break down than plums. John is willing to pay £10, 000 for a plum and £2, 000 for a lemon. Unfortunately, however, he cannot distinguish between the two types. Sellers can offer a warranty that would cover the full cost of any repair needed by the car for y ∗ years. Considering the type and likelihood of problems their cars can have, owners of plums estimate that y years of guarantee would cost them 1000y, owners of lemons estimate that the cost would be 2000y. John knows these estimates and decides to offer £10, 000 if a car comes with y ∗ years of warranty, £2, 000 if a car comes without warranty. For which values of y ∗ is there a separating equilibrium where only owners of plums are willing to offer the y ∗ -years warranty? Clearly explain your reasoning.

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 $_______. .

You have three tickets to a Celtics game on a night that you are going to be out of town (so the value of unsold tickets is zero to you). There are only four possible buyers of a Celtics ticket. The table below lists the respective reservation prices of these four possible buyers: Customer                     Reservation Price 1                                  $25 2                                  $35 3                                  $50 4                                  $60 You consider inviting bids using an English auction to sell your tickets. How much total revenue can you generate using the English auction mechanism from the sale of the three tickets? [Bids can be made in increments of $1.00]

Juanita is deciding whether to buy a skirt that she wants, as well as where to buy it. Three stores carry the same skirt, but it is more convenient for Juanita to get to some stores than others. For example, she can go to her local store, located 15 minutes away from where she works, and pay a marked-up price of $102 for the skirt:        Store Travel Time Each Way Price of a Skirt (Minutes) (Dollars per skirt) Local Department Store 15 102 Across Town 30 85 Neighboring City 60 76   Juanita makes $42 an hour at work. She has to take time off work to purchase her skirt, so each hour away from work costs her $42 in lost income. Assume that returning to work takes Juanita the same amount of time as getting to a store and that it takes her 30 minutes to shop. As you answer the following questions, ignore the cost of gasoline and depreciation of her car when traveling.