6.4. Revenue comparison. (a) Suppose there is one bidder, with value v1 U(0, 1). Derive the optimal take-it-orleave-it price to offer to this bidder in order to maximize expected revenue. (b) Now suppose there are two bidders, with values uniformly distributed on [0, 1]. Consider an SPSB auction with reserve price r = 1/2 (a reserve price works by requiring bids to be at least r, and setting the payment of the winning bidder to the maximum of r and the second highest bid). What is the expected revenue? Hint for part (b): break the revenue into cases depending on how the values relate to the reserve price (also known as a minimum bid) (c) Compare the expected revenue in (b) with the expected revenue in the standard SPSB auction, i.e., without using a reserve. What do you find? Explain why this observation is consistent with the revenue equivalence theorem