Auction theory: reserves vs. take-it-or-leave-it

[citrusvanilla]

hello,
i am under the impression that the take-it-or-leave-it ("buy it now") price that maximizes expected revenue to the seller is the same as the reserve price that maximizes revenue. this intuitively follows from setting both to the expected maximal realization of N players (for sake of problem, IID uniform on [0,1]). am i correct?

-justin

 

[citrusvanilla]

alternatively, by the same logic, the expected highest realization is not always 1/2, which is the maximum reserve price irrespective of the number of bidders, i.e. the highest realization of 100 players approaches 1