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

Answer 1

a)

probability that your bid will be accepted =(12000-9500)/(14600-9500)=0.49

b)

probability that your bid will be accepted=(14000-9500)/(14600-9500)=0.88

c)

amount should you bid to maximize the probability that you get the property (in dollars )=14600

d)

bid $12,750 to max your profit

e)

expected profit =(12750-9500)*(16000-12750)/(14600-9500)=2071.08