General equilibrium analysis:
Production
Lectures in Microeconomic Theory
Fall 2010, Part 13
07.07.2010
G.B. Asheim, ECON4230-35, #13
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Robinson Crusoe economy
Consumpt.
( p, w)
Output
Profitmaximizing
output
UtilityUtilit
maximizing
consumption
Labor
input
Leisure
Profit in
terms of
output
Utility-maximizing leisure Profit-maximizing labor input
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G.B. Asheim, ECON4230-35, #13
Equilibrium with production
Consumpt.
( p  , w )
Profitmaximizing
output
UtilityUtilit
maximizing
consumption
Labor
input
07.07.2010
Output
Utility-maximizing leisure
Profit in
Leisure terms of
Profit-maximizing output
labor input
G.B. Asheim, ECON4230-35, #13
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1
Overview of results
x12  x22
P

x1  x2
p  ( p1 , p2 )
x11  x12

Arrow-Debreu-McKenzie (1951–54)
If production sets are convex, and
utility functions are quasi-concave,
then an equilibrium exists.
Results in two-factor
two factor two
two-good
good economies w/CRTS:
(1) Increased price of one good leads to increased price
of the factor that is used more intensively in the production of that good. (The Stolper-Samuelson theorem)
(2) Increased supply of one factor leads to increased production of the good that is more intensive in the use of
this factor, for fixed output prices. (The Rybczynski theorem)
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G.B. Asheim, ECON4230-35, #13
1st welfare theorem holds …
Consumpt.
Output
Labor
input
Leisure
… even if the production set is not convex.
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G.B. Asheim, ECON4230-35, #13
2nd welfare theorem need not hold …
Consumpt.
Output
Labor
input
Leisure
… if the production set is not convex.
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G.B. Asheim, ECON4230-35, #13
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