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L12

L12. General Equilibrium. Review. Model of choice of individual We know preferences and we find demands With many such agents: Q1: How prices are formed? Q2: Are markets efficient?. “Economy” with apples and oranges. Two consumers, A and B.

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L12

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  1. L12 General Equilibrium

  2. Review • Model of choice of individual • We know preferences and we find demands • With many such agents: • Q1: How prices are formed? • Q2: Are markets efficient?

  3. “Economy” with apples and oranges • Two consumers, A and B. • Total resources available • Feasible allocation and

  4. Geometric representation • Four numbers and geometric representation • Insane? • No: Edgeworth box • Collection of all feasible allocations

  5. OB Edgeworth Box OA

  6. Desirable Allocation: Pareto Efficient • When allocation is “socially” efficient? - Maximizing sum of utilities? NO! - Weaker notion: Pareto efficiency! • Allocation x Pareto efficient, if there does not exist allocation y that is A) at least as good as x for all B) is strictly better for at least one

  7. OB Pareto Efficiency OA

  8. OB Pareto Efficiency=Tangenency OA

  9. OB Contract Curve • The contract curve is the set of all Pareto-optimal allocations. OA

  10. Cobb-Douglass example

  11. OB Contract Curve • The contract curve is the set of all Pareto-optimal allocations. OA

  12. How do Markets Work? How do markets work? • Individuals respond optimally to prices • Prices are such that markets clear We call a competitive equilibrium

  13. Excess supply, Demand OB OA

  14. Excess Demand, Supply, Equilibrium OB OA

  15. Excess Demand, Supply, Equilibrium OB OA

  16. Cobb-Douglass example

  17. Invisible Hand OB • Are markets (Pareto) efficient? • First Welfare Theorem: allocation in Competitive equilibrium is Pareto optimal • Proof OA

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