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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. Francis Edgeworth developed this method of analysis in the last portion of the 19th century.

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Edgeworth Box Analysis: Two Consumers

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  1. Edgeworth Box Analysis:Two Consumers Lecture 25 November 19 2002 Slides adapted from slide set for Microeconomics by Pindyck and Rubinfeld, Prentice Hall, 1998.

  2. 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.

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

  4. x2 y2 Here the axes for Jane have been rotated Jane y1 Bill x1

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

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

  7. y1 y1 0 0 x1 x1 Consider two consumers and two products Bill Jane

  8. The Edgeworth Box y1 y1 0 0 x1 x1

  9. The Edgeworth Box y1 y1 0 0 x1 x1

  10. The Edgeworth Box y1 y1 0 0 x1 x1

  11. The Edgeworth Box y1 y1 0 0 x1 x1

  12. The Edgeworth Box y1 y1 0 0 x1 x1

  13. The Edgeworth Box y1 y1 0 0 x1 x1

  14. The Edgeworth Box x2 III1 II1 I1 Jane y2 Trading area? A C I2 II12 III12 y1 Bill x1

  15. The Edgeworth Box x2 III1 II1 I1 Jane y2 A What about A here? C I2 II12 III12 y1 Bill x1

  16. The Edgeworth Box x2 III1 II1 I1 Jane y2 B PARETO OPTIMAL A C I2 II12 III12 y1 Bill x1

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

  18. 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

  19. Contract Line • Is the locus of Pareto optimal points

  20. The Edgeworth Box x2 IV2 III2 II2 I2 Jane y2 B E” E’ A E C y1 I1 II1 III1 IV1 Bill x1

  21. 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

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

  23. 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.

  24. 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.

  25. 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

  26. 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.

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

  28. 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.

  29. 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

  30. MARGINAL RATE OF SUBSTITUTION

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

  32. 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 NOW RETURN TO EDGEWORTH BOX ANALYSIS

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

  34. 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

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