1. (Optimal Reserve Price) A seller of cost 0 holds a sealed bid second price auction in which there are n bidders whose valuations are independent draws of a random variable that is uniformly distributed on [2, 3]. (a) Compute the seller's Optimal reserve price r*(c) for c E [0, 3]. (b) For what values of c is the seller's optimal reserve equal to the lowest possible buyer valuation? (c) Interpret the case where r*(c) is exactly equal to the lowest possible buyer valuation. (HINT: Consider the monopoly price on the inverse demand curve P(q) = 3 q)