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

Question

4. 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 $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part c (15,000)? Why or why not? (Hint: think about maximizing your profit from selling the property to that person.)

Explanation / Answer

Considering the uniform distribution formula, bidding less than 15000 means bidding at 14000, which would mean

14000-10000/15000-10000=4000/5000=0.8 probability of being accepted. Hence, it is not recommended to bid less than 15000 because that would also mean a 1-0.8=0.2 probability of bid not being accepted. In order to make profit on the property, one has to get it first. With 0.2 probability of not being accepted means there is a risk in commiting that property for 16000 to another buyer.

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