Suppose we are interested in bidding on a piece of land and we know one other bi

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 $10,400 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,100.

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?
$

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 $13,200. If your objective is to maximize the expected profit, what is your bid?
- Select your answer -Stay with your bid in part (c); it maximizes expected profitBid $13200 to maximize the expected profit

What is the expected profit for this bid (to 2 decimals)?
$

Explanation / Answer

1)Suppose you bid $12,000. What is the probability that your bid will be accepted =(12000-10400)/(15100-10400)

=0.3404

2)Suppose you bid $14,000. What is the probability that your bid will be accepted =(14000-10400)/(15100-10400)

=0.7660

3)What amount should you bid to maximize the probability that you get the property =15100

4) $13200 to maximize the expected profit

5) expected profit for this bid =(16000-13200)*(13200-10400)/(15100-10400)=1668.09

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