Problem
Patty Gonia is trying to sell a rain coat to two interested buyers, who each have value for the coat drawn independently from U[100,200].
I. If Patty sells the coat through a second price auction, what is her expected revenue? And what is the probability that she sells the jacket for at least $150 for sure?
II. What is the expected revenue in the ascending price auction?
III. Patty wonders whether setting a 'reserve price" would increase her expected revenue. A reserve price is a value R, where if the second price is below R then the item is sold at price R. If the highest bid is less than R, the item is not sold. What will Patty's expected revenue be if she runs a second price auction with reserve price R : $150? (Hint: look at the three case for how many bidders bid above $150. What is the probability that a bidder bids above $150? Also, note that given that a bidder bids above $150, their bid will be distributed U[150, 200].