PARETO EFFICIENCY
 Charles van Marrewijk
Edgeworth Box; 4
We can combine the information of these two figures into one figure
KX
0
KY
LX
0
LY
 Charles van Marrewijk
Edgeworth Box; 5
We can combine the information of these two figures into one figure
KX
0
LX
 Charles van Marrewijk
Edgeworth Box; 6
We can combine the information of these two figures into one figure
KX
0
LX
 Charles van Marrewijk
Edgeworth Box; 7
We can combine the information of these two figures into one figure
KX
0
LX
 Charles van Marrewijk
Edgeworth Box; 8
We can combine the information of these two figures into one figure
LY
0
KX
KY
0
LX
The Edgeworth Box
x2
Jane
y2
A
y1
Bill
x1
Total Fixed Supply of x
Total Fixed Supply of
y
Consider two consumers
and two products
y1
y1
0
0
x1
Bill
Jane
x1
The Edgeworth Box
y1
0
x1
y1
0
x1
The Edgeworth Box
y1
0
x1
y1
0
x1
The Edgeworth Box
y1
0
x1
The Edgeworth Box
y1
0
x1
The Edgeworth Box
y1
0
x1
The Edgeworth Box
0
x1
y1
y1
0
x1
The Edgeworth Box
x2
III1 II1
I1
Jane
y2
Trading area?
A
C
y1
Bill
x1
The Edgeworth Box
x2
III1 II1
I1
Jane
y2
A
What about A here?
C
y1
Bill
x1
The Edgeworth Box
x2
III1 II1
I1
Jane
B
y2
A
C
y1
Bill
x1
PARETO OPTIMAL
An Allocation is
Pareto Efficient/Optimal
• When no change can make one better off
without making the other worse off.
The Edgeworth Box
x2
IV2 III2 II2
I2
Jane
B
y2
E”
E’
Contract line
A
E
C
y1
Bill
x1
I1
II1
III1
IV1
Contract Line
• Is the locus of Pareto optimal points
The Edgeworth Box
x2
IV2 III2 II2
I2
Jane
B
y2
E”
E’
A
E
C
y1
Bill
x1
I1
II1
III1
IV1
The Edgeworth Box
x’2
III2 II2
x2
x”2
I2
Jane
y2
B
E”
E’
y’1
y’2
y”1
y”2
A
E
C
y1
Bill
x1
x’1
I1 II1 III1
x”1
Pareto improving-from A or B to E or
E”
The Edgeworth Box
x2
III2 II2
I2
Jane
y2
B
E”
E’
A
E
C
y1
Bill
x1
I1 II1
III1
Understanding the Picture
• Any point in the Edgeworth box indicates a
particular distribution of the two goods
among the two individuals, e.g., Bill and Jane.
• Each individual has an indifference curve
going through that point.
• If the distribution is Pareto optimal, those two
indifference curves are tangent at that point.
Prices that are consistent with the
Pareto optimal point
• At that tangency of the two indifference
curves, the slope of the tangency line--the
straight line drawn through the point of
tangency--represents the relative prices for
the two goods. Hence, there are relative
prices that will be consistent with the Pareto
optimum.
The Edgeworth Box
x2
III2 II2
I2
Jane
y2
B
E”
E’
A
Price or budget line
E
C
y1
Bill
x1
I1 II1
III1