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Economics 201A–Fall 2005–Second Half
The Second Welfare Theorem with Nonconvex Preferences
This handout is based on Anderson, “The Second Welfare Theorem with
Nonconvex Preferences,”
Econometrica
56(1988), 361382. As the diagram
on page 2 shows, the second welfare theorem may fail if preferences are
nonconvex. SpeciFcally, it gives an economy with two goods and two agents,
and a Pareto optimum
x
∗
so that so that the utility levels of
x
∗
cannot be
approximated by an Walrasian equilibrium with transfers; moreover, if
p
∗
is the price which locally supports
x
∗
,and
T
is the income transfer which
makes
x
a±ordable with respect to the prices
p
∗
, there is a unique Walrasian
equilibrium with transfers (
y
∗
,q
∗
,T
);
y
∗
is much more favorable to agent I
and much less favorable to agent II than
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 Spring '06
 ANDERSON
 Economics

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