Economics 201B–Second Half
Lecture 13
Justifying (or Undermining) the PriceTaking Assump
tion
•
Many formulations: Core, Ostroy’s No Surplus Condition, Bar
gaining Set, ShapleyShubik Market Games (noncooperative),
other noncooperative games
•
Core is the most commonly used. The
core
is the set of all
allocations such that no coalition (set of agents) can
improve
on
or
block
the allocation (make all of its members better
oF) by seceding from the economy and only trading among its
members.
•
Core is institutionfree; no mention of prices.
•
“Core convergence” means roughly that
For economies with a large number of agents, core
allocations are “approximately Walrasian.”
•
“Approximately Walrasian” means diFerent things in diFerent
contexts, depending on what we are willing to assume.
•
Three motivations for the study of the core
:
–
Walrasian allocations lie in the core
: Important strength
ening of ±irst Welfare Theorem, under same minimal as
sumptions as ±irst Welfare Theorem.
∗
(Positive): Strong stability property of Walrasian equi
librium: no group of individuals would choose to upset
the equilibrium by recontracting among themselves.
1
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(Normative): If distribution of initial endowments is eq
uitable, no group is treated unfairly at a core allocation.
Since Walrasian allocations lie in the core, this is a Group
Fairness Property of Walrasian Equilibrium.
–
Core Convergence strengthens Second Welfare Theorem
∗
Second Welfare Theorem says every Pareto Optimum is
a Walrasian Equilibria with Transfers.
∗
Core convergence asserts that core allocations of large
economies are
nearly
Walrasian
without
transfers.
∗
One version states that core allocations can be realized as
exact
Walrasian equilibrium with
small
income transfers.
∗
Strong “unbiasedness” property of Walrasian equilib
rium
·
Restricting to Walrasian outcomes does not narrow
possible outcomes beyond narrowing occurring in the
core.
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 Spring '06
 ANDERSON
 Economics, Game Theory, walrasian equilibrium

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