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 $9,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,500 and $14,600.

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 $12,750. If your objective is to maximize the expected profit, what is your bid? 1. stay with yourbid in part c: it maxmizes your profit 2.bid $12,750 to max your profit

Explanation / Answer

P( Bid of 12000 will win ) = P( competitor bids less than 12000) = (12000-9500)/(14600-9500) = 0.4901

P( Bid of 14000 will win ) = P( competitor bids less than 14000) = (14000-9500)/(14600-9500)= 0.8823

To maximise the prbabiltiy, we should be 14601 so that competitor has no chance of bidding

P( winning at 12750) =  (12750-9500)/(14600-9500) 0.6375

Expected profit = 0.6375*(16000-12750)= 2071.875

At our current bid of 14600, profit will be 1400

Hence, we should bid at 12750

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