Question

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,500 and $15,300. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)? Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)? What amount should you bid to maximize the probability that you get the property (in dollars)? Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,250. If your objective is to maximize the expected profit, what is your bid? SelectStay with your bid in part (c); it maximizes expected profitBid $13250 to maximize the expected profitItem 4 What is the expected profit for this bid (in dollars)?

Answer 1

1) e probability that your bid will be accepted =P(X<12000) =(12000-10500)/(15300-10500) =0.3125

2)  probability that your bid will be accepted =P(X<14000)=(14000-10500)/(15300-10500) =0.7292

3) maximize the probability that you get the property ; amount =15300

4) as (16000+10500)/2 =13250 whcih maximize profit

5) expected profit =Profit*probability =(16000-13250)*(15300-13250)/(15300-10500)= $1575.52