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
Utilitymaximizing
consumption
Labor
input
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Leisure
Profit in
terms of
output
Utility-maximizing leisure Profit-maximizing labor input
G.B. Asheim, ECON4230-35, #13
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1
Equilibrium with production
( p  , w )
Consumpt.
Profitmaximizing
output
Utilitymaximizing
consumption
Labor
input
Utility-maximizing leisure
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Profit in
terms
of
Leisure
Profit-maximizing output
labor input
G.B. Asheim, ECON4230-35, #13
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Overview of results
x12  x22
P

x1  x2
p  ( p1 , p2 )
x11  x12

Output
Arrow-Debreu-McKenzie (1951–54)
If production sets are convex, and
utility functions are quasi-concave,
quasi concave
then an equilibrium exists.
Results in two-factor two-good economies w/CRTS:
(1) Increased price of one good leads to increased price
of the factor that is used more intensively in the produc(Th Stolper-Samuelson
S l S
l theorem)
h
)
tion off that
h good.
d (The
(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)
07.07.2010
G.B. Asheim, ECON4230-35, #13
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2
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.
07.07.2010
G.B. Asheim, ECON4230-35, #13
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3