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Chapter 10: General Equilibrium
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So far, we have studied a partial equilibrium analysis,
which determines the equilibrium price and quantities in
one market.
It ignores the repercussions of a price change in that
market on equilibrium prices and quantities in other
markets.
A general equilibrium analysis traces the effects of a
change in demand or supply in one market on
equilibrium prices and quantities in all markets. Note that
if there are n goods, Xid=Xid(p1, p2, ……pn, Y).
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A general equilibrium exists when prices
have adjusted to a change in either
demand or supply so that quantities
demanded and quantities supplied are
equalized in all markets.
Used often in simulating the effect of policy
intervention in trade analysis and
environment literature.
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Example:
Corn & Soybean Markets
Corn Market
S
ec0
1
Pc
0
(0) Initial eq.: ec0, es0
(1) An external shock to
the corn demand, shifting
the demand from DC0 shifts
to DC1, causing PC to fall
(ec1)
DC0
ec1
Pc1
DC1
Soybean Market
(2) Consumers substitute
toward corn, away from
soybean, reducing the
demand for soybean from
Ds0 to Ds2
S
Ps0
Ps1
es0
2
es1
DS1
DS2
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(3) Because the price of corn
decreased relatively more than
the price of soybean did,
producers shift away from corn
to soybeans, shifting the
soybean supply curve to the
right, reaching es2.
(4) Because the decline of the price
of soybeans, producers now
produce more corn, shifting the
corn supply curve to the right
and reaching a new equilibrium.
(ec3)
Corn Market
SC0
4
DC0
Pc1
Pc2
ec3
DC1
Soybean Market
SS0
Adjustments continue…
SS2
3
(5) Because the decline of the price of
corn, consumers shift away from
soybeans, to DS4 and producers
produce more soybeans, shifting
the soybean supply curve to the
right, reaching es4.
SC3
5
Ps1
Ps2
DS1
es2
es
4
5
DS2
DS4
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Example:
Corn & Soybean Markets
• See the previous two
slides.
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Example: Minimum Wage Law
Minimum wage rate is imposed.
Initial wage rate.
Because of the high wage rate, the labor demand declines from L1C to L2C
The unemployed workers move to uncovered sectors.
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Example: Minimum Wage Law
Workers move to
uncovered sector,
decreasing the wage
rate.
Without the minimum
wage rate.
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Trading between Two People
• Suppose two people have two goods that
they may exchange if they wish.
• Their endowments:
Person A=(wA1, wA2), Person B=(wB1, wB2)
Good 1= wA1+ wB1, Good 2= wA2+ wB2
• Where do they end up?
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An Edgeworth box diagram
Person B
Good 2
W
Person A
Good 1
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An Edgeworth box diagram
Good 2
xA2
xB1
Person B
xB2
X
W
Person A
xA1
Good 1
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• They will trade until reaching to the Pareto optimum.
• Pareto optimum (efficient): an allocation of goods or
services such that one cannot be made better off without
worsening the other. This is where the MRS of two
people are equalized.
• The set of Pareto optimum points is called the “contract
curve.”
• Where they end up between the lens-shaped area
depends upon their bargaining power.
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x2A
x1
Contract Curve
ω1B
B
ω2B
ω2A
OA
OB
x1A
ω1A
The contract curve
x2B
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Competitive Exchange
• In a two-person exchange, the final allocation depends on
the bargaining power of the parties.
• However, when there are many sellers and buyers, each
participant acts as a price-taker.
• In the competitive markets, prices respond automatically
to excess demand and supply and will adjust until an
equilibrium is reached such that Qs=Qd (no excess
demand nor supply).
• Excess demand (supply) of a good puts pressure to raise
(lower) its relative price, reducing the quantity demanded
(supplied).
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Trade in Competitive Markets
For consumer A
Good2
p11A  p22A  p1 x1A  p2 x2A
MRS A  
p1
p2
x*2A
ω2A
OA
x*1A
ω1A
Good1
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For consumer B
Good2
p1  p2  p x  p x
B
1
MRS B  
ω2B
B
2
B
1 1
B
2 2
p1
p2
x*2B
OB
ω1B
x*1B
Good1
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• In competitive equilibrium: MRS A  P1  MRS B
p2
indicating that the competitive equilibrium should be on
the contract curve.
→ First welfare theorem: “The competitive equilibrium is
efficient.”
• Which Pareto-optimum is reached depends on the initial
endowment. Any Pareto-optimum bundle can be
obtained as a competitive equilibrium given an
appropriate endowment.
→ Second welfare theorem: “Any efficient allocations can
be achieved by competition.”
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Production and Trading
• We now consider the efficient use of inputs in
the production using GE analysis.
• Suppose food (F) and clothing (C) are produced
using labor (L) and capital (K). Total supply of L
and K are fixed in the society.
• An Edgeworth box diagram in production shows
every possible way that the existing K and L
might be used to produce F and C.
• We will use isoquants for the two goods.
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An Edgeworth Box Diagram in Production
Labor in C production
Labor for C
OC
Qf=15
Capital for C
Qf=10
Capital
in C
production
Capital
in F
production
Capital
for F
A
OF
Qc=12
Qc=10
Qc=7
Labor for F
Labor in F production
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• Many of the allocations in the Edgeworth box are
technically inefficient.
– it is possible to produce more F and more C by
shifting capital and labor around.
• The efficient allocations occur where the
isoquants are tangent to one another
(MRTSF=MRTSC) because output of one good
cannot be increased without decreasing the
output of another good in such allocations, i.e.,
Pareto optimum.
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Contract Curve in Production
At each efficient point (e), the MRTS is equal in
both Food and Clothing production
The contract curve
OC
C’’’’
e4
Total Capital
C’’’
e3
F’’’’
C’’
e2
C’
F’’’
e1
F’’
F’
OF
Total Labor
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• The locus of efficient points shows the maximum
output of C that can be produced for any level of
F..
• We can transfer this information to construct a
production possibility frontier (PPF).
• PPF shows the maximum amount of outputs (F
and C) that can be produced with the fixed
amount of inputs (K and L).
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Production Possibility Frontier
OC
Quantity of C
C’’’’
C’’’
e0
e1
C’
C’’
C’’
e2
C’
e3
C’’’
e4
e3
e2
F’’’
e1
F’
F’’’’
F’’
OF
e4
C’’’’
F’
F’’
F’’’
F’’’’
Quantity of F
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Production Possibility Frontier
If all resources are used to
produce C.
Quantity of C
e0
OC
C’’’’
C’’’
e1
C’
C’’
C’’
e2
C’
e3
C’’’
e4
e3
e2
F’’’
e1
F’
F’’’’
F’’
OF
e4
C’’’’
F’
F’’
F’’’
F’’’’
Quantity of F
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• Marginal Rate of Transformation of F for C (slope of
PPF):
– measures how much C must be given up to produce one
additional unit of F.
MRTof F for C  

MCF
C

F
MCC
As we increase the production of F by moving along the
PPF, the MRT increases in absolute value (or becomes
steeper), i.e., the PPF is concave.
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Clothes
Optimal Product Mix
Food
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• Output efficiency: For an economy to be efficient,
goods must be produced not only at minimum
cost but also to match people’s demands.
• An economy produces output efficiently only if,
for each consumer, MRS = MRT, i.e., the
conditions for the Pareto efficiency:
- P1/P2 = MRSA = MRSB = MRT
i.e., the rate at which firms can transform one
good into another = the rate at which consumers
are willing to substitute between the goods.
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Production and the Edgeworth Box Diagram
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Comparative Advantage
• The theory of comparative advantage
was first proposed by Ricardo
– Countries should specialize in producing
those goods of which they are relatively
more efficient producers
• these countries should then trade with the rest
of the world to obtain needed commodities
– If countries do specialize this way, total
world production will be greater.
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Efficient Choice of Output and Trade between
Two Countries
Which country is relatively efficient in producing good 1?
Good 2
Good 2
MRT= - 2/1
MRT= - 1/1
100
100
Good 1
50
Country A
50
Good 1
Country B
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Before trading, countries were producing at E0 and F0. Country A has
a comparative advantage in producing Good 2, while the country B has
a comparative advantage in producing Good 1.
Country A
Country B
Good 2
Good 2
F0
E0
IB
IA
50
100
Good 1
50
100
Good 1
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Suppose that the international price ratio of goods 1 and 2 is 2. Then,
country A produces at E1 and consumes at E2. Country B produces at
F1 and consumes at F2. Both countries are better off after the trade.
Country A
Good 2
Country B
F2
110
E1
100
IB
Import
Export
F1
60
E2
50
IA
P1/P2=2
P1/P2=2
50
100
Import
Good 1
50
100
Export
Good 1
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