U4, In this exercise, you will explore how much setting a reserve price can increase the seller's expected revenue. 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 V; r and V, rY X Prob(V, r (Region Ill), then bidder 2 wins and pays T'; this also happens with probability r r2. Finally, if V; > r and V, > r (Region IV), then the bidder with the higher value wins and pays the lower value; this happens with .. : . 2r+1 probability (1 )2, and when it happens, the price on average equals ?"3+.1 Region Il Region IV Bidder 2's private value, V, Region Il 0 r 1 Bidder 1's private value, V, (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 r. 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 r = % than when setting no reserve price? How much expected revenue is gained (or lost) by setting reserve price r = % ? 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 r = 34 than when setting no reserve price? How much expected revenue is gained (or lost) by setting reserve price r = 34? How often is the object left unsold