Problem 1. An “antique” table is for sale in a sealed bidauction. It will go to the high bidder at the price the high bidderbids. You don’t know if it is a fake or not, but you do know that20% of all antiques that look like this one are fakes. You are notable to have an appraiser examine it. If it is a fake, you willknow this after you buy it and it will be worthless to you. If itis real, it will be worth $1,000 to you.

You know that the only other possible bidder is an expertantique dealer has also looked at this table and you know that thisdealer can always tell a fake from a real antique. You know that ifthe antique dealer finds that it is a fake, she will bid zero forit. If she finds that it is real, she will bid $500 for it if shehas a similar table in stock, and will $800 for it if she hasanother table like it in stock. Suppose that you believe that it isequally likely that the dealer has another table like it instock.

A) What do you believe is the probability that the antiquedealer will bid $500 for the table? What do you believe is theprobability that she will bid $800 for the table?

B) If you bid $300 for the table and you are the high bidder,what is your probability that the table is a genuine antique? Whatis your expected profit (or loss) if you bid $300?

C) If you bid $501 for the table, what is the probability thatyou will be the high bidder. What is the probability that the tableis genuine if you bid $501 and are the high bidder? What is yourexpected profit (or loss) if you bid $501?

D) If you bid $801 for the table, what is the probability thatyou will be the high bidder? What is your expected value for thetable if you are the high bidder? What is your expected profit (orloss) if you bid $801?

E) Suppose you could choose to bid any amount between 0 and$1000 for the table. What bid would maximize your expected payoff?Explain your answer.