1) Late in the day at an auction house there are only two bidders left, April and Bart. Th last item, a second-hand sound system in excellent condition, is brought out, and each bidder takes a look at it. The seller says she will accept sealed bids from each bidder and will sell the sound system to the highest bidder at the highest bidder's bid Each bidder believes that the other is equally likely to value the sound system at any amount between $0 and $1500.00. Therefore, for any number, x, between $0 and $1500.00 each bidder believes that the probability that the other bidder values the sound system less than x is x/1500.00. The sound system is worth $1150.00 to April. If she gets the sound system, her profit will be the difference between $1150.00 and what she pays fom it, and if she does not get the sound system, her profit will be zero. She wants to make her bid in a such a way as to maximize her expected profits. i) Suppose that April thinks that Bart will bid exactly what the sound system is worth to him. If she bids $1050.00, what will be her expected profit? ii) Suppose that Bart will bid exactly what the sound system is worth to him. If April bids $950.00, what is her expected profit in this case? Again, suppose that Bart will bid exactly what the sound system is worth to him. Suppose that April bids $x for the sound system (where x is a number between $0 and $1500.00). What is the x that would maximize April's expected ii)
1) Late in the day at an auction house there are only two bidders left, April and Bart. Th last item, a second-hand sound system in excellent condition, is brought out, and each bidder takes a look at it. The seller says she will accept sealed bids from each bidder and will sell the sound system to the highest bidder at the highest bidder's bid Each bidder believes that the other is equally likely to value the sound system at any amount between $0 and $1500.00. Therefore, for any number, x, between $0 and $1500.00 each bidder believes that the probability that the other bidder values the sound system less than x is x/1500.00. The sound system is worth $1150.00 to April. If she gets the sound system, her profit will be the difference between $1150.00 and what she pays fom it, and if she does not get the sound system, her profit will be zero. She wants to make her bid in a such a way as to maximize her expected profits. i) Suppose that April thinks that Bart will bid exactly what the sound system is worth to him. If she bids $1050.00, what will be her expected profit? ii) Suppose that Bart will bid exactly what the sound system is worth to him. If April bids $950.00, what is her expected profit in this case? Again, suppose that Bart will bid exactly what the sound system is worth to him. Suppose that April bids $x for the sound system (where x is a number between $0 and $1500.00). What is the x that would maximize April's expected ii)
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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Transcribed Image Text:1) Late in the day at an auction house there are only two bidders left, April and Bart. The
last item, a second-hand sound system in excellent condition, is brought out, and each
bidder takes a look at it. The seller says she will accept sealed bids from each bidder and
will sell the sound system to the highest bidder at the highest bidder's bid.
Each bidder believes that the other is equally likely to value the sound system at any
amount between $0 and $1500.00. Therefore, for any number, x, between $0 and $1500.00,
each bidder believes that the probability that the other bidder values the sound system
less than x is x/1500.00. The sound system is worth $1150.00 to April. If she gets the
sound system, her profit will be the difference between $1150.00 and what she pays for
it, and if she does not get the sound system, her profit will be zero. She wants to make
her bid in a such a way as to maximize her expected profits.
i)
Suppose that April thinks that Bart will bid exactly what the sound system is
worth to him. If she bids $1050.00, what will be her expected profit?
ii)
Suppose that Bart will bid exactly what the sound system is worth to him. If
April bids $950.00, what is her expected profit in this case?
Again, suppose that Bart will bid exactly what the sound system is worth to
him. Suppose that April bids $x for the sound system (where x is a number
between $0 and $1500.00). What is the x that would maximize April's expected
profit?
iii)
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