Lecture Notes,
May 9, 2011  Part 1
General Equilibrium in an Economy with unbounded technology sets
Delete P.VI (bounded
j
).
Like all good mathematicians, we're reducing this to
the previous case.
Under assumptions of No Free Lunch (P.IV(a))
and Irreversibility (P.IV(b)), the
attainable output set for the economy and for each firm is still bounded.
P.IV. (a)
if
for some k.
y
Y
and
y
0, then
y
k
0
(b)
if .
y
Y
and
y
0, then
y
Y
Let firm j's (unbounded) production technology be Y
j
.
Define S
j
(p) as j's profit
maximizing supply in Y
j
.
Define D
i
(p) as i's demand without restriction to
{x x
c} and with income M
i
(p)=
.
Note that S
j
(p) and D
i
(p)
p
r
i
j
ij
j
p
may not be well defined.
Define
= Y
j
{x x
c}, substitute
for
j
in chapters 11  14.
Define
(p)
Y
j
Y
j
S
j
as j's supply function based on
.
Y
j
Theorem 15.3(b):
If
(p) is attainable, then S
j
(p) =
(p).
S
j
S
j
Theorem 16.1(b):
If
M
i
(p) =
, and
(p) is attainable, then
(p) = D
i
(p).
M
i
p
D
D
Z(p) =
i
D
i
(p) 
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 Fall '08
 ZAMBRANO
 Economics, Microeconomics, Equilibrium, Supply And Demand, Economic equilibrium, yj, Prof. R. Starr, artificially bounded economy

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