3. The original Filene’s Basement in Boston had a unique pricing system. Every article in the store was marked with a tag showing the price and the date the article was first put on sale. Twelve days later, if it had not been sold, the price was reduced by 25 percent. Six selling days later, it was cut by 50 percent, and after an additional 6 days, it was offered at 75 percent off the original price. After 6 more days, it was given to charity if it had not been sold.

a. Was the Filene’s plan similar to any of the auctions we studied in this chapter?

b. Suppose you are interested in a coat you have seen in a store that uses the same pricing system as Filene’s Basement. (“The Basement” closed its doors in 2011.) The initial price is $200. You are willing to pay as much as $150. Could it be optimal to buy the coat when the price is reduced to $150? Could it be optimal to wait 6 days and try to buy the coat when the price is reduced to $100? Could it be optimal to wait 12 days and try to buy the coat when the price is reduced to $50?