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 $9,700 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,700 and $14,700.

a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?

c. What amount should you bid to maximize the probability that you get the property (in dollars)?

d. 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 $12,850. If your objective is to maximize the expected profit, what is your bid?

What is the expected profit for this bid (in dollars)?

Answer 1

a)

probability that your bid will be accepted=(12000-9700)/(14700-9700)==0.46

b)probability that your bid will be accepted=(14000-9700)/(14700-9700)=0.86

c)

to maximize probability one should bid =14700

d)

bid =(16000-9700)/2+9700=12850

expected profit =(16000-12850)*(12850-9700)/(14700-9700)=1984.50