1. Bulow and Klemperer (1996) showed the expected revenue ofN+ 1bidders without a reserve price is strictly higher than the expected revenue ofNbidders with the optimal reserve price, i.e., E[max{(X1), (X2), ..., (XN+1)}]> E[max{(X1), (X2), ..., (XN),0}].

(a)Check this withN= 2andFU[0,1]. That is, calculate LHS and RHS in the above inequality.

(b)Does the result also hold with aasymmetricbidders? That is, either prove

E[max{1(X1), 2(X2), ..., N+1(XN+1)}]> E[max{1(X1), 2(X2), ..., N(XN),0}],or find an example where this does not hold.