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CHAPTER 30 EXCHANGE

CHAPTER 30 EXCHANGE. Partial equilibrium analysis: The equilibrium conditions of ONE particular market, leaving other markets untreated. General equilibrium analysis: The equilibrium conditions of ALL markets, allowing interactions between different markets. 30.1 The Edgeworth Box.

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CHAPTER 30 EXCHANGE

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  1. CHAPTER 30EXCHANGE

  2. Partial equilibrium analysis: The equilibrium conditions of ONE particular market, leaving other markets untreated. • General equilibrium analysis: The equilibrium conditions of ALL markets, allowing interactions between different markets.

  3. 30.1 The Edgeworth Box • Two consumers: A and B. • Two goods: 1 and 2. • Initial endowment: • Allocation: • Feasible allocation: total consumption does not exceed total endowment for both goods.

  4. 30.1 The Edgeworth Box

  5. 30.1 The Edgeworth Box • Each point in the Edgeworth box represents a feasible allocation. • From W to M: • Person A trades units of good 1 for units of good 2; • Person B trades units of good 2 for units of good 1.

  6. 30.2 Trade

  7. 30.2 Trade • Trade happens whenever both consumers are better off. • Starting from W, M is a possible outcome of the exchange economy because: • Person A is strictly better off with than with ; • Person B is strictly better off with than with .

  8. 30.3 Pareto Efficient Allocations • An allocation is Pareto efficient whenever: • There is no way to make everyone strictly better off; • There is no way to make some strictly better off without making someone else worse off; • All of the gains from trade have been exhausted; • There are no (further) mutually advantageous trades to be made.

  9. 30.3 Pareto Efficient Allocations

  10. 30.3 Pareto Efficient Allocations • Pareto efficiency is given by the tangency of the indifference curves. • Contract curve: the locus of all Pareto efficient allocations. • Any allocation off the contract curve is Pareto inefficient.

  11. 30.4 Market Trade • Gross demand: Quantity demanded for a good by a particular consumer at the market price. • Excess demand: The difference between the gross demand and the initial endowment of a good by a particular consumer. • Disequilibrium: Excess demands by both consumers do not sum up to zero.

  12. 30.4 Market Trade

  13. 30.4 Market Trade • Competitive equilibrium: A relative price and an allocation , such that: • The allocation matches the gross demands by both consumers, given the relative price and initial endowments; • The allocation is feasible.

  14. 30.4 Market Trade

  15. 30.5 The Algebra of Equilibrium • Consumer A’sdemands: • Consumer B’sdemands: • The equilibrium condition: • Re-arrangement:

  16. 30.5 The Algebra of Equilibrium • Net demand: • Aggregate excess demand: • Another expression:

  17. 30.6 Walras’ Law • Budget constraints: • Re-arrange the terms: • Adding up:

  18. 30.6 Walras’ Law • Walras’ Law: The value of aggregate excess demand is always zero. • Applications of the Walras’ law: • implies ; • Market clearing for one good implies that of the other good; • With k goods, we only need to find a set of prices where k-1 of the markets are cleared.

  19. 30.7 Relative Prices • Walras’ law implies k-1 independent equations for k unknown prices. • Only k-1 independent prices. • Numeraire prices: the price which can be used to measure all other prices. • If we choose p1 as the numeraire price, then it is just like multiplying all prices by the constant t=1/p1.

  20. EXAMPLE: An Algebraic Example of Equilibrium • The Cobb-Douglas utility function: • The demand functions:

  21. EXAMPLE: An Algebraic Example of Equilibrium • Income from endowments: • Aggregate excess demand for good 1:

  22. EXAMPLE: An Algebraic Example of Equilibrium • Equilibrium condition: • Equilibrium price:

  23. 30.8 The Existence of Equilibrium • The existence of a competitive equilibrium can be proved rigorously. • A formal proof is quite complicated and far beyond the scope of this course.

  24. 30.9 Equilibrium and Efficiency • Both indifference curves are tangent to the budget line at the equilibrium allocation. • The equilibrium allocation lies upon the contract curve. • The First Theorem of Welfare Economics: Any competitive equilibrium is Pareto efficient.

  25. EXAMPLE: Monopoly in the Edgeworth Box • A regular monopolist

  26. EXAMPLE: Monopoly in the Edgeworth Box • First degree price discrimination

  27. 30.11 Efficiency and Equilibrium • Reverse engineering: • Starting from any Pareto efficient allocation; • Use the common tangent line as the budget line; • Use any allocation on the budget line as the initial endowment. • The Second Theorem of Welfare Economics: For convex preferences, any Pareto efficient allocation is a competitive equilibrium for some set of prices and some initial endowments.

  28. 30.11 Efficiency and Equilibrium • The Second Theorem of Welfare Economics

  29. 30.11 Efficiency and Equilibrium • A Pareto efficient allocation that is not a competitive equilibrium.

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