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.1 The seller announced that the highest bid in excess of $10,000 will be accept­ ed. Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000.

a. Suppose you bid $12,000. what is the probability that your bid will be accepted?

b. Suppose you bid $14,000. what is the probability that your bid will be accepted?

c. what amount should you bid to maximize the probability that you get the property?

d. 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)? why or why not?

Explanation / Answer

Since the competitor's bid X is a random variable that is uniformly distributed between $10,000 and $15,000.

We have the following density function:
f(x) = 1/(15,000-10,000) = 1/5000, 10,000 <= X <=15000; 0, elsewhere

(a) The probablility that a $12,000 bid will be accepted, P(10,000 < x < 12,000) = 2000/5000 = .40

(b) The probablility that a $14,000 bid will be accepted, P(10,000 < x < 14,000) = 4000(1/5000) = .80

(c) To to maximize the probability that you get the property, you need to make P=1. This happens if you bid $15,000. Actually you need to bid $ 15,001, knowing that the competitor's bid can't exceed $ 15,000.

(d) You should NOT consider bidding less than the amount shown in part (c) as that maximises your probability of winning the deal.

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