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, 100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10, 100 and $15, 300. 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, 050. 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( bid of $12000 getting accepted) = (12000-10100)/(15300-10100)

= 0.37

B) P($14000 bid getting accepted) =(14000-10100)/(15300-10000)

= 0.75

C) $15300

P($15300 bid = 1)

D) P($13050 bid getting accepted) = (13050-10100)/(15300-10100)

= 0.57

Expected profit = 0.57x(16000-13050) = $1674

Expected profit for bid of $15300 = $700

So, bid of $13050 will give more profit than bid of $15300

Expected profit = $1674

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