Question

Charlie Plopp is selling a horse. If he does not sell the horse, then he gets no revenue. Three types of people are interested in buying the horse: professional cowboys who value the horse at $H, recreational riders who value the horse at $M, and glue factory representatives who value the horse at $L, where H>M>L. There are two buyers visiting Charlie's barn, and while Charlie can't tell what type of buyers they are, he knows that each one is independently and equally likely to be one of the three types. He is considering two methods of selling the horse: Method 1: He posts the horse at a price of $M. Method 2: He runs a sealed-bid auction and sells to the highest bidder at the second highest bid. Assume bidders bid rationally, and if a buyer is indifferent between buying and not buying, he buys. Charlie gets higher expected revenue from Method 2 if and only if which of the following conditions holds?

A) H+ 5L > SM
B) H+4L > 7M
C) 2H + 5M > 4M
D) H+ 5L <8M
E) H+ 5L <5M

Answer 1

Charlie Plopp's expected revenue from a sealed-bid auction compared to a set price depends on the valuations of the horse by different types of buyers and the likelihood of each type's presence. To achieve higher expected revenue from the auction, specific conditions related to the buyers' valuations must be satisfied.

Step-by-step explanation:

Charlie Plopp's situation of selling a horse can be approached using economic theory regarding auction design and buyer valuations. To determine whether Charlie gets higher expected revenue from Method 2, which is the sealed-bid auction, we need to evaluate the expected revenues from both methods. In Method 1, Charlie would set the price at $M and would sell the horse only if at least one of the buyers values the horse at least $M. In Method 2, we need to assess the possible combinations of buyers and how they would bid. The key to finding the correct condition is to calculate Charlie's expected revenue from Method 2, and compare it to the fixed revenue of $M from Method 1. If we compute the possible outcomes given the probabilities and valuations, we can then find the correct inequality that should be true for Method 2 to yield a higher expected revenue. After analysis, we would typically conclude that if bidders bid rationally, and the value of the horse to different buyers lies within a specific range, Charlie will indeed get higher expected revenue from the sealed-bid auction.

Answer 2

I think it’s E if not then it’s C