It is otherwise equal to 1. Knowing this, rewrite (6.3.29) as
It follows that σ= 1/3. Observe
Hence, in this example, the second-best mechanism employs the allocation rule:
In words, exchange occurs if and only if the buyer’s valuation exceeds the seller’s cost
by at least one-quarter of the buyer’s maximum valuation. Figure 6.4 illustrates for the
case in which
¯
b=¯c
(“should” in the figure means if the first best is to be achieved).
45
6.3.3 The Money-on-the-Table Problem
From Proposition 6.13, the best outcome when subject to interim IR is exchange
whenever
V
B
(b,σ)
≥
V
C
(c,
σ)
. Unless σ= 0, there exist v ...
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