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Edgeworth Box Analysis: Two Consumers. Lecture 25 November 19 2002 Slides adapted from slide set for Microeconomics by Pindyck and Rubinfeld, Prentice Hall, 1998. The Edgeworth Box Analysis. Francis Edgeworth developed this method of analysis in the last portion of the 19th century.

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edgeworth box analysis two consumers

Edgeworth Box Analysis:Two Consumers

Lecture 25

November 19 2002

Slides adapted from slide set for Microeconomics by Pindyck and Rubinfeld, Prentice Hall, 1998.

the edgeworth box analysis
The Edgeworth Box Analysis
  • Francis Edgeworth developed this 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.
to form and edgeworth box
To Form and Edgeworth Box
  • Rotate one of the graphs onto the other one until it forms a box.
slide6

The Edgeworth Box

x2

Jane

y2

A

Total Fixed Supply of y

y1

Bill

x1

Total Fixed Supply of x

slide7

y1

y1

0

0

x1

x1

Consider two consumers and two products

Bill Jane

slide14

The Edgeworth Box

x2

III1 II1 I1

Jane

y2

Trading area?

A

C

I2 II12 III12

y1

Bill

x1

slide15

The Edgeworth Box

x2

III1 II1 I1

Jane

y2

A

What about A here?

C

I2 II12 III12

y1

Bill

x1

slide16

The Edgeworth Box

x2

III1 II1 I1

Jane

y2

B

PARETO OPTIMAL

A

C

I2 II12 III12

y1

Bill

x1

pareto optimal
Pareto Optimal
  • When no change can make one better off without making the other worse off.
slide18

The Edgeworth Box

x2

IV2 III2 II2 I2

Jane

y2

B

E”

E’

Contract line

A

E

C

y1

I1 II1 III1 IV1

Bill

x1

contract line
Contract Line
  • Is the locus of Pareto optimal points
slide20

The Edgeworth Box

x2

IV2 III2 II2 I2

Jane

y2

B

E”

E’

A

E

C

y1

I1 II1 III1 IV1

Bill

x1

slide21

The Edgeworth Box

x’2x”2

x2

III2 II2 I2

Jane

y2

B

E”

E’

Pareto improving--from A or B to E or E”

y’2

y”2

y’1

y”1

A

E

C

y1

I1 II1 III1

Bill

x1

x’1x”1

slide22

The Edgeworth Box

x2

III2 II2 I2

Jane

y2

B

E”

E’

A

E

C

y1

I1 II1 III1

Bill

x1

understanding the picture
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
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.
slide25

The Edgeworth Box

x2

III2 II2 I2

Jane

y2

B

E”

E’

A

Price or budget line

E

C

y1

I1 II1 III1

Bill

x1

tangent line is really a budget line for both individuals
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 Jane is IJane = Pxxjane + PyyJane where I is the income Jane could get from selling the X and Y she holds at the Pareto optimum point.
budget line for jane
Budget Line for Jane

Ijane/Py

IJane = Pxxjane + PyyJane

E

Price or budget line

C

y

Jane

Ijane/Px

x

marginal rate of substitution
Marginal Rate of Substitution
  • MRSxy = the number of units of y one is willing to give up per unit of x and stay on same indifference curve.
  • Slope of indifference curve gives the marginal rate of substitution.
marginal rate of substitution1
Marginal Rate of Substitution

Slope of indifference curve gives the marginal rate of substitution

Ijane/Py

D

Price or budget line

y

Jane

Ijane/Px

x

at point d
At point D
  • Slope of indifference curve equals the slope of the budget line or
  • MRSxy = -Px/ Py
now return to edgeworth box analysis
At point E’, the indifference curve for Jane is just tangent to the indifference curve for Bill, and the price line is the tangency line at E. In other words, Slope(Indifference curve for Jane) = Slope(Indifference curve for Bill) = Slope of price lineNOW RETURN TO EDGEWORTH BOX ANALYSIS
slide34

The Edgeworth Box

x2

III2 II2 I2

Jane

y2

B

E”

E’

A

Price or budget line

E

C

y1

I1 II1 III1

Bill

x1