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The Edgeworth Box and Pareto Optimal
Presented By:Sudhir Kale.MITCON Institute of management, Pune.
The Edgeworth Box
Francis Edgeworth developed the method of analysis in the last portion of the 19th century.
Provides a powerful way of graphically studying exchange and the role of markets.
Understanding the Edgeworth Box is critical to understanding exchange and markets.
The modern version of diagram is commanly referred to as Edgeworth-Bowley box.
How To Form an Edgeworth Box
Rotate one of the graphs onto the other one until it forms a box.
Consider two consumers and two products
x1
y1
0x1
y1
0
y1
x1
y2
x2
The Edgeworth Box
x1
y1
0
x1
y1
0
The Edgeworth Box
x1
y1
0
x1
y1
0
The Edgeworth Box
x1
y1
0
x1
y1
0
The Edgeworth Box
x1
y1
0
x 1
y 1 0
The Edgeworth Box
x1
y1
0
x1
y1
0
The Edgeworth Box
x1
y1
0
x1
y1
0
Pareto Optimal
When no change can make one better off without making the other worse off.
With general equilibrium of production & exchange, economic efficiency is maximum & we have Pareto Optimal.
According to this concept, a distribution of inputs among commodities & of commdities among consumer is Pareto Optimal or efficient.
The Edgeworth Box
x1
y1
y2
x2
I 2
II 12
III 12
III1 II1 I1
A
C
A is the equilibrium point where pareto optimum occuring.
The Edgeworth Box
x1
y1
y2
x2
I1 II1 III1 IV1
IV2 III2 II2 I2
A
B
C
E
E’
E”
Contract lineWhich is locus of all Pareto optimals.
Understanding the Picture
Any point in the Edgeworth box indicates a particular distribution of the two goods among the two individuals, e.g. A and B.
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.
The Edgeworth Box
x1
y1
y2
x2
I1 II1 III1
III2 II2 I2
A
B
C
E
E’
E”
Price or budget line
Tangent line is really a budget line for both individuals
If one extends the tangent line to each axis, we now have a budget line.
For example, the budget line for 1st individual is where I is the income that person get from selling the X and Y he/she holds at the Pareto optimum point.
x
y
C
E
Price or budget line
Income/price of x
Inco
me/
pri
ce o
f y
Budget Line
x
y
D
Price or budget line
Income/Px
I nco
me/P
y
Marginal Rate of Substitution
Slope of indifference curve gives the marginal rate of substitution
MARGINAL RATE OF SUBSTITUTION
yofutilityinalm
xofutilityinalmMRSxy arg
arg
xofUtilityinalMMRS
arg
At point D
Slope of indifference curve equals the slope of the budget line or
MRSxy = -Px/ Py
