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 $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 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?
$

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 $13,000. If your objective is to maximize the expected profit, what is your bid?
- Select your answer -Stay with your bid in part (c); it maximizes expected profitBid $13000 to maximize the expected profitItem 4

What is the expected profit for this bid (to 2 decimals)?
$

Answer 1

a) Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

=(12000-10000)/(15300-10000) = 0.38

b)

(14000-10000)/(15300-10000) = 0.75

c)

to maximize winning (probablity of winning1) bid should be theheighest = 15300

d)

At 13000 the probablity of winning is (13000-10000)/(15300-10000) = 0.57

Expected profit at 13000 = Revenue from selling the property - Cost of bid= 16000 - x, to maximize xpected profit, bid lowest

Expected profit = 0.57*(16000-13000) = 1710