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.

P(12000 winning) = 1-(15400-12000)/(15400-9800) =1-0.604=0.39.

P(14000 winning) =1- (15400-14000)/(15400-9800) = 0.75

c.

I shold bid More than $15,400

d.

P(12900 winning) = 1- (15400-12900)/(15400-9800) = 0.55

Expected profit = 0.55*(16000-12900) = $1705

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