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Chapter 21

Chapter 21. The Problem of Exchange. Objective. Given an economy where individuals are allocated a certain amount of goods, we will Investigate barter exchange d efine equilibrium trade Investigate the emergence of competitive markets . Harvesting & Gathering: Need for Trade.

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Chapter 21

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  1. Chapter 21 The Problem of Exchange

  2. Objective • Given an economy where individuals are allocated a certain amount of goods, we will • Investigate barter exchange • define equilibrium trade • Investigate the emergence of competitive markets

  3. Harvesting & Gathering: Need for Trade • Primitive, two-person economy • Geoffrey, Elizabeth • Harvest & gather fruit • Apples, raspberries • Voluntary trade – beneficial • Options • Consume all • Trade some

  4. Edgeworth Box & Feasible Trades • Edgeworth box • Graphical device to analyzethe process of trade • Its size equals the total amount of goods • A point in the box represents a possible/ feasibleallocation of goods

  5. Edgeworth Box & Feasible Trades • No-trade allocation • Feasible allocation • No trade • Individuals consume their own harvest

  6. The Edgeworthbox: Dimensions 10 Apples 0 8 Raspberries Dimensions of the Edgeworth box represent total amount of each good. There are 10 apples and 8 raspberries

  7. The Edgeworth box: Geoffrey and Elizabeth Raspberries to Elizabeth Elizabeth 6 0 10 f 8 2 Apples to Elizabeth Apples to Geoffrey I1e 0 2 8 I1g Raspberries to Geoffrey Geoffrey

  8. Finding Equilibrium Trades • Equilibrium allocation • Once reached • No incentive to further trade • Block • Prevent a trade • Coalition – each gets more • Individually rational trade • Higher utility - than no trade

  9. Utility-improving trades Raspberries to Elizabeth 6 4 0 f g 10 i h j 8 2 Apples to Elizabeth Apples to Geoffrey 4 6 I3e I3g I1e I2e I2g 0 2 4 8 I1g Raspberries to Geoffrey The shaded, lens-shaped area represents the set of allocations that do not lower either agent’s utility relative to the no-trade allocation at point f .

  10. Efficient / Pareto-Optimal Allocation • Pareto-optimal (efficient) allocation • Allocation of goods across people • No other allocation can make one person better off without making the other worse off. • Not efficient allocation • Indifference curves cross • Efficient allocation • Indifference curves - tangent

  11. Marginal Conditions for Efficient Trades • Efficient allocation • Tangency point - indifference curves • Marginal rates of substitution - same • Contract curve • Curve in Edgeworth box • All efficient trades

  12. The contract curve Raspberries to Elizabeth l k OE Apples to Geoffrey Apples to Elizabeth Raspberries to Geoffrey OG The contract curve is a locus of all efficient trades, i.e., of all tangency points

  13. The contract curve • Contract curve • Set of efficient/ Pareto optimal trades • No more voluntary trade will take place.

  14. The Core of an Economy Raspberries to Elizabeth C l k f m Blocked by Elizabeth OE n Apples to Geoffrey Apples to Elizabeth Blocked by Geoffrey I1e Raspberries to Geoffrey I1g OG A The shaded, lens-shaped area represents the set of allocations that do not lower either agent’s utility relative to the no-trade allocation at point f .

  15. Marginal Conditions for Efficient Trades • Core of economy • Set of equilibrium trades • Portion of contract curve • Between no-trade indifference curves • Individually rational • Cannot be blocked

  16. A Growing Population and the Core • Economy – grows through replication • As we add agents • Set of core allocation – diminish • Points on original core – eliminated

  17. The core of a four- person economy 5 6 Raspberries to Elizabeth C n z f m Apples to Geoffrey Apples to Elizabeth 5 2 1 2 1 2 3 8 7 2 Raspberries to Geoffrey 2 3 A G1 and G2 will negotiate with E2 a better deal: Each G offers 2.5 apples and gets in return 0.5 raspberries

  18. An Economy with Many Agents • Economy – grows larger • Set of core allocations – one point • Competitive behavior • Price-taking behavior • Individuals take prices as given • Based on the value of their endowments decide how much of each good to buy • Competitive Equilibrium • Set of prices that clear markets (QD=QS of each good) • Determined by the endowment and individual preferences

  19. A Competitive Equilibrium Raspberries to Elizabeth f C e Apples to Geoffrey Apples to Elizabeth Raspberries to Geoffrey A

  20. Not A Competitive Equilibrium Raspberries to Elizabeth z f B C Apples to Geoffrey y Apples to Elizabeth Raspberries to Geoffrey D A Point e

  21. Conditions for Competitive Equilibrium • A Competitive Equilibrium is defined by a set of prices such that • For any good • Total Quantity demanded= Total Quantity Supplied • At those prices

  22. Conditions for Competitive Equilibrium • To solve: • Find the demand for each good by each individual • Use the utility function • Individual income evaluated at the competitive prices • Calculate market demand by adding up all individual demand • Total supply is total amount of good i. • Set total demand = total supply

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