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 $9,800 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,800 and $15,400.

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 $12,900. If your objective is to maximize the expected profit, what is your bid? What is the expected profit for this bid (in dollars)?

Explanation / Answer

a)

12000-9800/15400-9800

2200/5600

0.3928

b)

14000-9800/15400-9800

4200/5600

0.75

c)

$15400 or more

d)

(16000-12900)*(3-12900/5000)

3100*0.42

1302

When sold for 16000, it is 1000.

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