Asked by Nur Farzana Binti Hasrunlah A19A0553 on May 12, 2024
Verified
A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $200.There are two bidders.The dealer believes that there are only three possible values that each bidder's willingness to pay might take, $7,700, $3,100, and $200.Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the automobile is
A) $2,600.
B) $5,400.
C) $3,666.67.
D) $3,100.
E) $7,700.
Reservation Price
The highest price a person is prepared to spend on a product or service.
English Auction
A bidding process where the price ascends and the highest bid wins, commonly used in auction houses and online marketplaces.
Willingness To Pay
The maximum amount an individual is prepared to spend on a good or service, reflecting the perceived value.
- Understand thoroughly the concept and the mechanisms that govern English auctions.
- Review the estimated revenue streams from auctions with assorted reservation price points.
- Absorb the techniques employed by bidders in auctions that prohibit collusion.
Verified Answer
VV
Violet VetterMay 13, 2024
Final Answer :
C
Explanation :
For the dealer to sell the automobile, the highest bidder's bid must exceed the reservation price of $200. If one of the bidders has a willingness to pay of $7,700 or $3,100, the dealer will receive a payment of $7,700 or $3,100. If the highest bid is $200, the dealer will not sell the automobile.
Let's consider the possible scenarios:
- Both bidders have a willingness to pay of $7,700: In this case, the auction will end with a bid of $7,700 and the dealer will receive a payment of $7,700.
- One bidder has a willingness to pay of $7,700 and the other has a willingness to pay of $3,100: In this case, the auction will end with a bid of $7,700 and the dealer will receive a payment of $7,700.
- One bidder has a willingness to pay of $7,700 and the other has a willingness to pay of $200: In this case, the auction will end with a bid of $7,700 and the dealer will receive a payment of $7,700.
- One bidder has a willingness to pay of $3,100 and the other has a willingness to pay of $7,700: In this case, the auction will end with a bid of $3,100 and the dealer will receive a payment of $3,100.
- Both bidders have a willingness to pay of $3,100: In this case, the auction will end with a bid of $3,100 and the dealer will receive a payment of $3,100.
- One bidder has a willingness to pay of $3,100 and the other has a willingness to pay of $200: In this case, the auction will end with a bid of $3,100 and the dealer will receive a payment of $3,100.
- Both bidders have a willingness to pay of $200: In this case, the dealer will not sell the automobile.
The expected revenue for the dealer is the sum of the probabilities of each scenario multiplied by the revenue from that scenario:
E(revenue)=19(7700)+29(3100)=346009≈3,666.67E(revenue) = \frac{1}{9}(7700) + \frac{2}{9}(3100) = \frac{34600}{9} \approx 3,666.67 E(revenue)=91(7700)+92(3100)=934600≈3,666.67
Therefore, the best choice is (C).
Let's consider the possible scenarios:
- Both bidders have a willingness to pay of $7,700: In this case, the auction will end with a bid of $7,700 and the dealer will receive a payment of $7,700.
- One bidder has a willingness to pay of $7,700 and the other has a willingness to pay of $3,100: In this case, the auction will end with a bid of $7,700 and the dealer will receive a payment of $7,700.
- One bidder has a willingness to pay of $7,700 and the other has a willingness to pay of $200: In this case, the auction will end with a bid of $7,700 and the dealer will receive a payment of $7,700.
- One bidder has a willingness to pay of $3,100 and the other has a willingness to pay of $7,700: In this case, the auction will end with a bid of $3,100 and the dealer will receive a payment of $3,100.
- Both bidders have a willingness to pay of $3,100: In this case, the auction will end with a bid of $3,100 and the dealer will receive a payment of $3,100.
- One bidder has a willingness to pay of $3,100 and the other has a willingness to pay of $200: In this case, the auction will end with a bid of $3,100 and the dealer will receive a payment of $3,100.
- Both bidders have a willingness to pay of $200: In this case, the dealer will not sell the automobile.
The expected revenue for the dealer is the sum of the probabilities of each scenario multiplied by the revenue from that scenario:
E(revenue)=19(7700)+29(3100)=346009≈3,666.67E(revenue) = \frac{1}{9}(7700) + \frac{2}{9}(3100) = \frac{34600}{9} \approx 3,666.67 E(revenue)=91(7700)+92(3100)=934600≈3,666.67
Therefore, the best choice is (C).
Learning Objectives
- Understand thoroughly the concept and the mechanisms that govern English auctions.
- Review the estimated revenue streams from auctions with assorted reservation price points.
- Absorb the techniques employed by bidders in auctions that prohibit collusion.