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 $9,800 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,800 and $15,300.

1. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
2. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
3. What amount should you bid to maximize the probability that you get the property (in dollars)?
   
   
4. 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 $12,900. If your objective is to maximize the expected profit, what is your bid?
   Select Stay with your bid in part (c); it maximizes expected profit / Bid $12900 to maximize the expected profit
   
   What is the expected profit for this bid (in dollars)?

Answer 1

1
=(15300-12000)/(15300-9800)=0.6

2
=(14000-12000)/(15300-9800)=0.363636363636364

3
=15300=15300

4.
Expected profit for bid of 12900=(12900-12000)/(15300-9800)*(16000-12900)=507.2727273

Expected profit for bid of 15300=700

Stay with your bid in part (c); it maximizes expected profit

Expected profit=700