University of Minnesota
Department of Economics
Econ 3102 : Intermediate Macroeconomics
Handout 3
This handout presents how we can use all the results obtained in handouts 1 and 2 in order
ll do this in two di/erent routes: following
1 Competitive equilibrium
In class we gave the de±nition of competitive equilibrium, now we can do it mathsmatically:
Def:
A
competitive equilibrium
is a set of
(
C;N
s
;N
d
;T;Y;w
)
such that given
(
G;z;K;h
)
:
1. The representative consumer chooses
C;‘
to solve
max
C;‘
U
(
C;‘
)
s.t.
C
=
w
(
h
‘
) +
T
C
±
0
0
²
‘
²
h
where
N
s
=
h
‘
.
2. The representative ±rm chooses
N
d
to solve
max
N
d
zF
(
K;N
d
)
wN
d
s.t.
N
d
±
0
where
Y
=
zF
(
K;N
d
)
,
=
Y
wN
d
=
zF
(
K;N
d
)
wN
d
.
1
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View Full Document3. All markets clear:
N
d
=
N
s
:
G
=
T:
2 Characterizing the competitive equilibrium
U
‘
(
C;‘
)
wU
C
(
C;‘
) = 0
(1)
wN
s
+
T
C
= 0
:
(2)
zF
N
(
K;N
d
) =
w;
(3)
and ±nally, we need the market clearing condition, plus the government budget constraint:
N
d
=
N
s
(4)
G
=
T:
(5)
N
d
=
N
s
=
N
, and substitute in (2),
(3). Then we get:
wN
+
T
C
= 0
(6)
zF
N
(
K;N
) =
w:
(7)
2
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 Spring '11
 erick
 Economics, representative, competitive equilibrium, Economic equilibrium

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