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 $14,800.

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?

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

Answer 1

1)Suppose you bid $12,000. What is the probability that your bid will be accepted =(12000-10500)/(14800-10500)=0.35

2)Suppose you bid $14,000. What is the probability that your bid will be accepted =(14000-10500)/(14800-10500)=0.81

3)

What amount should you bid to maximize the probability that you get the property=14000

4)you should bid =(16000+10500)/2=13250

5) expected profit for this bid =(13250-10500)*(16000-13250)/(14800-10500)=1758.72