where the first equality follows via integration by parts. To summarize the analysis to
this point:
Lemma6.10.A necessary and sufficient condition for a direct-revelation mechanism to be
interim individually rational is that expression(6.3.26)be non-negative.
The second-best problem can now be stated:
subject to the constraints that (6.3.26) be non-negative,
¯
c
c
x(b,c)g(c)dc
be nondecreas-
ing in b, and
¯
b
0
x(b,c)f(b)db
be nonincreasing in c. In light of Proposition 6.12, the
constraint that expression (6.3.26) be non-negative is binding. Let λ > 0 be the Lagrange
multiplier ...
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