EC 11 Homework Problem

      Eleven condominiums are for sale.  There are four two-bedroom condos seven one-bedroom condos. (Actually there are 14 but 3 of the one BR are held off of the market as indicated by the high “min”  of 999,000). The condos are going to be sold to the highest bidder in a simultaneous progressive auction.  That is, all markets are open and people begin to bid the prices up.  The auction stops when no one is willing to place more bids.  That is, bidding continues until it stops naturally.

    There are 14 bidders and each wants one and only one condo.  Obviously there are more bidders than condos so three bidders are going to be unable to buy.  The values these bidders place on the condos are in the table below.  The table shows the value of each bidder for a two BR property and the value of the same bidder for a one BR unit.  As it turns out there is alternative housing available at zero charge for everyone who might want it but it is not especially desirable.  The table includes that value that the bidders place on the alternative housing.
 

Personal id code (PIC)	2 BR  value of individual	1 BR value of individual	Alternative Housing value of individual
954	990000	814000	264000
961	990000	814000	264000
957	968000	792000	264000
965	946000	792000	264000
953	902000	814000	264000
967	902000	814000	264000
958	880000	814000	264000
968	880000	814000	264000
951	836000	792000	264000
962	836000	792000	264000
960	836000	792000	264000
966	814000	770000	264000
955	726000	704000	330000
970	726000	704000	330000

     The results of the auction are on the accompanying table below.  These are data from an experiment conducted on October 19,1999.   For each property the table shows the final auction price.  However, the auction ended on a claimed error.  Bidder 967 had a browser problem (the auction was online) and was unable to place a bid. Not knowing that 967 wanted to bid again the auctioneer closed the auction.
     Imagine the following. The seller is upset, claiming that the carelessness of the auctioneer cost the seller a great deal of money because had the auction continued the price of the 2 BR condos would have increased to 638000 and the price of the 1BR condos would have been 506000. The auctioneer claims that the seller’s assertions are silly and had the auction continued there would have been no more than an additional bid or two and that he owes the seller nothing, not even an apology.

     Who is correct and why?  (Hint: The seller is correct according to the principles used in the book.  The problem for you is to explain why or to give a better model.) The model claims that if one more 1BR had been offered the prices would have been 462,000 for the 2BR and 374 for the 1 BR.  Can you support or disprove that claim?