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Partial Equilibrium and Welfare Analysis
Econ 210C
UCSB
May 16, 2011
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View Full Document Partial Equilibrium Analysis
Two Goods: the consumption good and the numeraire (e.g.,
expenditures on other goods).
Endowments:
ω
i
= (
0,
ω
im
)
,
i
=
1, 2,
···
,
n
.
Preferences:
u
i
(
x
i
,
m
i
) =
φ
i
(
x
i
) +
m
i
,
i
=
1, 2,
···
,
n
.
Production Technology:
C
j
(
q
j
)
denotes the amount of the
numeraire needed to produces
q
j
units of the consumption
good.
Relative Shares:
θ
ij
,
i
=
1,
···
,
n
,
j
=
1,
···
,
m
.
A competitive equilibrium can be identiﬁed by the equilibrium
price and quantities of the consumption good consumed by the
consumers and produced by the ﬁrms.
Econ 210C UCSB
Paper
φ
i
is diﬀerentiable and concave and
C
j
is
diﬀerentiable and convex.
Utility Maximization:
max
x
i
[
φ
i
(
x
i
) +
ω
im
+
Proﬁt Share

px
i
]
. By the
KhunTucker Theorem, a solution satisﬁes
φ
0
i
(
x
i
)

p
≤
0
and
[
φ
0
(
x
i
)

p
]
x
i
=
0.
(1)
Proﬁt Maximization: max
q
j
[
pq
j

C
j
(
q
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This note was uploaded on 12/26/2011 for the course ECON 210C taught by Professor Qin during the Fall '09 term at UCSB.
 Fall '09
 QIN

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