Two bidders = 1,2 have (uncorrelated) private values that are uniformly distributed over the interval from 0 to 1. The figure below illustrates the four basic possible outcomes. First, if 1 and 2 ) (2 (Region III), then bidder 2 wins and pays ; this also happens with probability 2. Finally, if 1 > and 2 > (Region IV), then the bidder with the higher value wins and pays the lower value; this happens with probability (1 )2, and when it happens, the price on average equals (2+1)/3. (a) What is the seller's expected revenue without any reserve price? (b) Provide a formula expressing the seller's expected revenue as a function of . Hint: Determine the probability that bidder values fall in each of the four possible regions shown in the figure and the expected price (with price = 0 if no sale is made) when values fall in each region. (c) Does the seller earn more expected revenue, less expected revenue, or the same amount when setting a reserve price = than when setting no reserve price? How much expected revenue is gained (or lost) by setting reserve price = ? How often is the object left unsold? (d) Does the seller earn more expected revenue, less expected revenue, or the same amount when setting a reserve price = than when setting no reserve price? How much expected revenue is gained (or lost) by setting reserve price = ? How often is the object left unsold? 1 When two bidders have private values uniformly drawn from an interval [, ], the higher value, on average, equals ( + 2)/3 while the lower value, on average, equals (2 + )/3. When bidder values are in Region IV, they are each drawn from the interval [, 1].