  We study surplus extraction in the general environment of McAfee and Reny
(1992), and provide two alternative proofs of their main theorem. The first is
an analogue of the classic argument of Cremer and McLean (1985, 1988), using
geometric features of the set of agents' beliefs to construct a menu of
contracts extracting the desired surplus. This argument, which requires a
finite state space, also leads to a counterexample showing that full extraction
is not possible without further significant conditions on agents' beliefs or
surplus, even if the designer offers an infinite menu of contracts. The second
argument uses duality and applies for an infinite state space, thus yielding
the general result of McAfee and Reny (1992). Both arguments suggest methods
for studying surplus extraction in settings beyond the standard model, in which
the designer or agents might have objectives other than risk neutral expected
value maximization.
