General Equilibrium and Economic Welfare
Perloff Chapter 10
General Equilibrium
• Partial equilibrium– Changes in equilibrium are analysed in one (or
a few) markets in isolation.– Prices and quantities in ‘unrelated’ markets are
held fixed.
• General equilibrium– The study of how equilibrium is attained in all
markets simultaneously.
GE in Corn and Soya Beans
Soybeans, Billion bushels per year
e0s
e2s
e4s
D4s
D2s
S4s
S2s
S0s
D0s
$4.12
$3.8325$3.8180
2.072.05142.0505
(b) Soybean Market
Corn, Billion bushels per year
e0c
e1c
e3c
D0c
D1c
S3c
S0c
$2.15
$1.9171$1.9057
8.448.26138.227
(a) Corn Market
Pric
e, $
per
bus
hel
Pric
e, $
per
bus
hel
Min. wages with incomplete coverage
L, Annual hours
(a) Covered Sector (b) Uncovered Sector (c) Total Labor Market
w1 w1 w1
w2
w–
S
Lc2 Lc
1 Lu2Lu
1 Lc1 Lu
1L1 = +
D c Du
S u
D
Lc , Annual hours Lu , Annual hours
w, W
age
per
hour
w, W
age
per
hour
w, W
age
per
hour
Trade Between People: The Edgeworth Box
I1jI1d
(a) Jane’s Endowment
Jane’s candy20
30
Candy, Bars
0j
ej
(b) Denise’s Endowment
Denise’s candy60
20
Candy, Bars
0d
edFir
ewo
od,
Co
rds
Fir
ewo
od,
Co
rds
(c) Edgeworth Box
Jane’s candy
Denise’s candy
C
A
B
20 40
608050
30e
a
f
8050
30
20
0j
0d
I1j
I1d
Jane
’s w
ood
Den
ise’s w
oo
d
Obtaining the contract curve
Jane’s candy
Denise’s candy
20 40
608050
30
20
40
g
c
d
e
b
a
f
B
8050
30
20
Contract curve
0j
0d
I1j
I 2jI 3j
I 4j
I 0d
I1d
I 2d
I 3d
Jane
’s w
ood
Denise’s w
ood
Four equivalent statements about points on the contract curve
• The indifference curves are tangential.
• The marginal rates of substitution are equal.
• No further mutually beneficial trades are possible.
• The allocation is Pareto efficient: One person cannot be made better off without making the other worse off.
Price that doesn’t lead to equilibrium
80
(b) Prices That Do Not Lead to a Competitive Equilibrium
Jane’s candy
Denise’s candy
Price line
20 30
608050
30
45
22
43
e
a
j
d
6050
32
20
0j
0d
I1j
I 2j
I1d
I 2d
Denise’s w
ood
Jane
’s w
ood
Price that leads to equilibrium(a) Price Line That Leads to a Competitive Equilibrium
Jane ’ s candy
Denise’s candy
Price line
20 40
608050
30
40
20
40
e
a
f
8050
30
20
0j
0d
I1j
I 2j
I1d
I 2d
Jane
’s w
ood
Denise’s w
ood
• The competitive equilibrium is Pareto efficient.
• Any efficient allocations can be achieved by competition.– Any point on the contract curve can be achieved by
trade along the appropriate price line.– Achieving the desired point may involve some
redistribution (value judgements required)
Theorems of Welfare Economics
cj d
w
pMRS MRS
p
Production Possibilities
I 1
I 2
PPF
80
50
Candy, Bars
a
b
Fir
ew
oo
d,
Co
rds
c
w
MCMRS MRT
MC
Competition Ensures Efficiency
c
c c
w w
c c
w w
c
w
pMRS
p
p MC
p MC
p MCMRT
p MC
pMRS MRT
p
The whole picture
c c
w w
p MCMRT
p MC
’
Price line
PPF
1
80 Candy, Bars0j
1–2
–
Fire
wo
od
, C
ord
s
50a
Janes candy
Jan
e’s
wo
od
40
Ij
Id
Price line
40
1
1–2
–
40
20 30f
Denise’s candy
De
nise
’s wo
od
c
w
pMRS
p
Is efficiency enough?
• Many policies make somebody better off at the expense of somebody else.
• Producer surplus plus consumer surplus.– As long as producers gain more than consumers
lose, its efficient eg. first degree price discrimination.
– Weights producers and consumers equally.
Utility possibilities frontier
UPF
Jane’s utility
Den
ise’
s ut
ility
Jane s candy
Denise’s candy
0j
0d
Jane
’s w
ood
Denise’s w
ood
Welfare maximisation
UPF UPF
c
a
b
e
(a)
Jane’s utility
W 1 W 2
W 3
(b)
Jane’s utility
W 1 W 2 W 3
Den
ise’
s ut
ility
Den
ise’
s ut
ility
How do we arrive at a social preference ranking
• Individuals rankings are transitive• We need a rule which allows us to convert individual rankings into a social
ranking.– Majority voting
• 2 prefer a to b, 2 prefer b to c, transitivity would require 2 to prefer a to c.• But 2 prefer c to a.
Voting with non-transitive prefrences
• With non-transitive preferences result depends on order the vote is taken in.• a compared to b then compare winner to c
– a chosen in first vote– c chosen in second vote
• c compared to a then compare winner to b– c chosen in first vote– b chosen in second vote
Arrow’s impossibility theorem
• Desirable properties of a social preference ordering.– Complete– If everyone prefers a to b, the social ranking should do
the same– Social ranking of a to b should not depend on the what
other alternatives are available– Dictatorship is not allowed
• No rule exists which produces a ranking that always satisfies these properties
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