The Edgeworth Box

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

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