1. Alles nur geklaut?!
Die folgenden Folien wurden erstellt von Arlo Biere, Kansas State University

2. Edgeworth Box Analysis: Two Consumers
Lecture 25
November
Slides adapted from slide set for Microeconomics by Pindyck and Rubinfeld, Prentice Hall, 1998.

3. 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.

4. To Form and Edgeworth Box
Rotate one of the graphs onto the other one until it forms a box.

5. Here the axes for Jane have been rotatedy2
Jane y1
Bill x1

6. Move axes for Jane to close box
Bill
Jane x2 y2 y1 x1

7. The Edgeworth Box x2 Jane y2 A Total Fixed Supply of y y1 Bill x1
Total Fixed Supply of x

8. Consider two consumers and two productsx1 y1 x1 y1
Bill Jane

9. The Edgeworth Box x1 y1 x1 y1

10. The Edgeworth Box x1 y1 x1 y1

11. The Edgeworth Box x1 y1 x1 y1

12. The Edgeworth Box x1 y1 x1 y1

13. The Edgeworth Box x1 y1 x1 y1

14. The Edgeworth Box x1 y1 x1 y1

15. The Edgeworth Box x2 III1 II1 I1 Jane y2 Trading area? A I2 II12 III12C
I II III12 y1
Bill x1

16. The Edgeworth Box x2 III1 II1 I1 Jane y2 A What about A here?C
I II III12 y1
Bill x1

17. The Edgeworth Box x2 III1 II1 I1 Jane y2 B PARETO OPTIMAL AC
I II III12 y1
Bill x1

18. Pareto Optimal
When no change can make one better off without making the other worse off.

19. The Edgeworth Box x2 IV2 III2 II2 I2 Jane y2 B E” E’ Contract line A E
I II1 III IV1
Bill x1

20. Contract Line
Is the locus of Pareto optimal points

21. The Edgeworth Box x2 IV2 III2 II2 I2 Jane y2 B E” E’ A E C y1
I II1 III IV1
Bill x1

22. Pareto improving--from A or B to E or E”
The Edgeworth Box
x’ x”2 x2
III2 II 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’ x”1

23. The Edgeworth Box x2 III2 II2 I2 Jane y2 B E” E’ A E C y1 I1 II1 III1
Bill x1

24. 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.

25. 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.

26. 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

27. 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.

28. Budget Line for Jane Ijane/Py IJane = Pxxjane + PyyJane E
Price or budget line C y
Jane
Ijane/Px x

29. 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.

30. 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

31. MARGINAL RATE OF SUBSTITUTION

32. At point D
Slope of indifference curve equals the slope of the budget line or
MRSxy = -Px/ Py

33. 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 line

34. The prices (ratio of prices) can produce the optimum

35. 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