Question

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.1 The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000. a. Suppose you bid $12,000. What is the probability that your bid will be accepted? b. Suppose you bid $14,000. What is the probability that your bid will be accepted? c. What amount should you bid to maximize the probability that you get the property? d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

Answer 1

The competitor’s bid is a random variable that is uniformly distributed between $10,000 and $15,000.The PDF is

a)You bid $12,000. The probability that your bid will be accepted is the event when your competitors bid is less than  $12,000. That is

b)You bid $14,000. The probability that your bid will be accepted is the event when your competitors bid is less than  $14,000. That is

c) To maximize the probability (make it eqiual to 1) that you get the property, you bid more than $15,000. Competitors maximum bid.

d) Since $16,000 > $15,000, you can bid for just more than $15,000.