ECON GU4260 - MARKET DESIGN Columbia University - Department of Economics Problem Set 1 1. Consider an auction with two bidders. Each bidder's valuation v is drawn as follows: With probability % the valuation v is distributed uniformly between 0 and % With probability % the valuation v is distributed uniformly between % and 1. (a) If we run a first price auction, what is the optimal bid function of a bidder with valuation v;? (b) What is the expected revenue of the seller? (c) Suppose now that there is only one bidder and that the seller runs a second price auction with a reserve price. Calculate the optimal reserve price