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.

I need the answers in TWO decimal places to not be wrong.

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 (in dollars)? =14800

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 $13,250. If your objective is to maximize the expected profit, what is your bid? =(16000+10500)/2=13250

5)

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