You want to auction off a good of no value to you. You know the value to every potential

bidder is distributed uniformly on [0; $8], independently across bidders. To get any bidders

to come to your auction, you must exert costly effort. Specifically, for every $1 you spend on

recruitment, you get one extra bidder. Once the recruitment is over, the bidders arrive (and

see how many of them are there). They then bid for your good in a second-price auction

(with no reserve price). Bidders are risk-neutral. How much should you spend on bidder

recruitment (to maximize your expected revenue net of the recruitment costs)?

How would the answer change if you used a first-price auction (with no reserve price) instead?