Economics 201B–Second Half
Lecture 14
Uncertainty, including GEI Model
•
GEI (General Equilibrium, Incomplete Markets) Model studies
situations in which markets are incomplete: there are restric
tions on the allowed trades
•
Six Models
V(a): DC
V(b): DI
↑
III: REE
IV: GEI
II: A
↑
I: AD
–
AD: ArrowDebreu complete contingent claims
–
A: Arrow securities
–
REE: Rational Expectations Equilibrium
–
GEI: General Equilibrium, Incomplete Markets
–
DC: Dynamic Completeness
–
DI: Dynamic Incompleteness
•
Model I: Complete Set of ArrowDebreu Contingent Claims
–
L
physical goods (umbrellas, houses)
–
States
s
= 1
, . . . , S
States reﬂect the set of possible situations (rainy, sunny, my
house burns, doesn’t burn)
1
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–
At time 0, don’t know which state
s
will prevail at time
1, but do know the set of states and the probability dis
tribution over the states. Trade “contingent commodities”
(an umbrella if it rains, a house if my house burns). You
buy a piece of paper (security) which you can turn in for
an umbrella if it rains, and is worthless otherwise.
–
At time 1, the state
s
is revealed. You turn in your state
s
securities for goods, the securities for the other states are
worthless, there is no trade, consumption occurs.
–
Formally, a statecontingent commodity bundle is
(
x
11
, . . . , x
L
1
, x
12
, . . . , x
L
2
, . . . , x
1
S
, . . . , x
LS
)
∈
R
LS
+
where
(
x
1
s
, . . . , x
Ls
)
is the consumption if state
s
occurs.
–
Point: Create
LS
goods, just like an economy with no un
certainty. The Existence and Welfare Theorems and their
proofs hold verbatim provided
∗
There is a market for each of the
LS
statecontingent
commodities; and
∗
Either
·
Everyone knows the true probability distribution over
states (no private information); or
·
Everyone agrees on the probability distribution over
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 Spring '06
 ANDERSON
 Economics, Fundamental theorems of welfare economics

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