Question

In: Advanced Math

Jane wants to auction off an item, but does not know where to go to find...

Jane wants to auction off an item, but does not know where to go to find bidders. David offers to find bidders for her, but will charge her $10 per bidder he gets to show up. Each bidder will uniformly value the item between [500. 1000). The highest bidder will win the item and pay the second-highest bidder's price (Vickrey auction). How many bidders should Jane pay David to find?

Expert Solution

according to the given question, bidders bid uniformaly between 500 and 1000. For each bidder jane pays 10$ to david.

solution:

suppose there are 'n' bidders to be found,

1st bidder starts from 500.

difference of price between bidders = 500/(n-1); since the range has to be divided into (n-1) parts for n bidders to be from 500 till just before 1000. Here, i am considering the highest price to be as close to 1000 so that Jane gets as much price of the item as possible.

item price

p = price given by (n-1)^th bidder. - 10*n;

differentiating P w.r.t n to get the optimum value of n ;

equating dp/dt = 0, and solving for n, we get n = 8 as one possibel number of bidders that will increase the profir of Jane.

hope the solution is clear and please ask any query if there is some.

Thank you.

Colby Messinger answered 1 year ago

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