General Equilibrium and Economic Welfare

1
General Equilibrium and Economic Welfare

• Perloff Chapter 10

2
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.

3
GE in Corn and Soya Beans
(a) Corn Market
c
S
0
c
S
3
c
e
0
2.15
Price, per bushel
c
D
0
c
e
c
1
e
1.9171
3
1.9057
c
D
1
8.44
8.2613
8.227
Corn, Billion bushels per year
(b) Soybean Market
s
S
0
s
e
0
4.
12
Price, per bushel
s
D
0
s
S
2
s
S
4
s
e
2
3.8325
3.8180
s
e
4
s
D
2
s
D
4
2.07
2.0514
2.0505
Soybeans, Billion bushels per year
4
Min. wages with incomplete coverage
(a) Covered Sector
(b) Uncovered Sector
(c) Total Labor Market
w, Wage per hour
w, Wage per hour
w, Wage per hour
S
w

u
S
w
w
w
1
1
1
w
2
c
u
D
D
D
2
1
2
1
1
1
L
L
L
L
L
L
L


c
c
u
u
c
u
1
L
, Annual hours
L
, Annual hours
L
, Annual hours
c
u
5
Trade Between People The Edgeworth Box
(a) Jane

s Endowment
(b) Denise

s Endowment
e
Firewood, Cords
Firewood, Cords
j
30
e
d
20
1
I
d
1
I
j
0
0
20
60
j
d
Jane

s candy
Denise

s candy
Candy, Bars
Candy, Bars
6
Obtaining the contract curve
Denise

s candy
60
80
40
0
d
50
g
Denises wood
0
Contract curve
I
d
d
4
I
1
I
e
j
d
30
20
2
I
d
c
3
I
f
d
20
30
B
3
I
j
b
2
I
j
1
I
j
Janes wood
a
50
0
20
40
80
j
Jane

s candy
7
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.

8
Price that doesnt lead to equilibrium
(b) Prices That Do Not Lead to a Competitive
Equilibrium
Denise

s candy
60
80
43
0
d
50
45
Denises wood
1
I
e
d
30
20
2
I
d
j
22
d
32
2
I
j
1
I
j
Janes wood
Price line
a
50
0
80
20
30
60
j
Jane

s candy
9
Price that leads to equilibrium
(a) Price Line That Leads to a Competitive
Equilibrium
Denise

s candy
60
80
40
0
d
50
Denises wood
40
1
I
e
d
20
30
2
I
d
f
20
30
2
I
j
1
I
j
Janes wood
Price line
a
50
0
20
40
80
j
Jane

s candy
10
Theorems of Welfare Economics

• 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)

11
Production Possibilities
2
I
Firewood, Cords
1
I
PPF
a
50
b
80
Candy, Bars
12
Competition Ensures Efficiency
13
The whole picture
Price line
1
Firewood, Cords


2
1
PPF
a
50
0
80
Candy, Bars
j

14
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.

15
Utility possibilities frontier
Denise

s candy
0
d
Denises utility
UPF
Denises wood
Janes wood
0
j
Jane
s candy
Jane

s utility
16
Welfare maximisation
(a)
(b)
a
Denises utility
Denises utility
UPF
UPF
e
b
3
W
2
W
1
W
1
2
3
W
W
W
c
Jane

s utility
Jane

s utility
17
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.

18
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

19
Arrows 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