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General Equilibrium and Economic Welfare

General Equilibrium and Economic Welfare. Perloff Chapter 10. General Equilibrium. Partial equilibrium Changes in equilibrium are analysed in one (or a few) markets in isolation. Prices and quantities in ‘unrelated’ markets are held fixed. General equilibrium

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General Equilibrium and Economic Welfare

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  1. General Equilibrium and Economic Welfare Perloff Chapter 10

  2. General Equilibrium • Partial equilibrium • Changes in equilibrium are analysed in one (or a few) markets in isolation. • Prices and quantities in ‘unrelated’ markets are held fixed. • General equilibrium • The study of how equilibrium is attained in all markets simultaneously.

  3. (a) Corn Market c S 0 GE in Corn and Soya Beans c S 3 c e 0 $2.15 Price, $ per bushel c D 0 c e c 1 e $1.9171 3 $1.9057 c D 1 8.227 8.2613 8.44 Corn, Billion bushels per year (b) Soybean Market s S 0 s e 0 $4. 12 Price, $ per bushel s D 0 s S 2 s S 4 s e 2 $3.8325 $3.8180 s e 4 s D 2 s D 4 2.0505 2.0514 2.07 Soybeans, Billion bushels per year

  4. Min. wages with incomplete coverage (a) Covered Sector (b) Uncovered Sector (c) Total Labor Market w, Wage per hour w, Wage per hour w, Wage per hour S w – u S w w w 1 1 1 w 2 c u D D D 2 1 1 2 1 1 L L L L L = L + L c c u u 1 c u L , Annual hours L , Annual hours L , Annual hours c u

  5. (c) Edgeworth Box Denise ’ s candy 80 60 0 d 50 Denise’s wood A 1 I d e 30 20 f 30 B C Jane’s wood 1 I j a 50 0 20 40 80 j Jane ’ s candy Trade Between People: The Edgeworth Box (a) Jane ’ s Endowment (b) Denise ’ s Endowment Firewood, Cords Firewood, Cords e j 30 e d 20 1 I d 1 I j 0 0 20 60 j d Jane ’ s candy Denise ’ s candy Candy, Bars Candy, Bars

  6. Obtaining the contract curve Denise ’ s candy 80 60 40 0 d 50 g Denise’s wood 0 Contract curve I d d 4 I 1 I e j d 30 20 2 I d c 3 I f d 20 30 B 3 I j b 2 I j 1 I j Jane’s wood a 50 0 20 40 80 j Jane ’ s candy

  7. Four equivalent statements about points on the contract curve • The indifference curves are tangential. • The marginal rates of substitution are equal. • No further mutually beneficial trades are possible. • The allocation is Pareto efficient: One person cannot be made better off without making the other worse off.

  8. Price that doesn’t lead to equilibrium (b) Prices That Do Not Lead to a Competitive Equilibrium Denise ’ s candy 80 60 43 0 d 50 45 Denise’s wood 1 I e d 20 30 2 I d j 22 d 32 2 I j 1 I j Jane’s wood Price line a 50 0 20 30 60 80 j Jane ’ s candy

  9. Price that leads to equilibrium (a) Price Line That Leads to a Competitive Equilibrium Denise ’ s candy 80 60 40 0 d 50 Denise’s wood 40 1 I e d 20 30 2 I d f 20 30 2 I j 1 I j Jane’s wood Price line a 50 0 20 40 80 j Jane ’ s candy

  10. Theorems of Welfare Economics • The competitive equilibrium is Pareto efficient. • Any efficient allocations can be achieved by competition. • Any point on the contract curve can be achieved by trade along the appropriate price line. • Achieving the desired point may involve some redistribution (value judgements required)

  11. Production Possibilities 2 I Firewood, Cords 1 I PPF a 50 b 80 Candy, Bars

  12. Competition Ensures Efficiency

  13. Denise ’ s candy 40 I j 40 Denise’s wood I d f 20 30 Price line Jane’s wood 1 – – 2 1 40 Jane s candy The whole picture Price line 1 Firewood, Cords – – 2 1 PPF a 50 0 80 Candy, Bars j ’

  14. Is efficiency enough? • Many policies make somebody better off at the expense of somebody else. • Producer surplus plus consumer surplus. • As long as producers gain more than consumers lose, its efficient eg. first degree price discrimination. • Weights producers and consumers equally.

  15. Utility possibilities frontier Denise ’ s candy 0 d Denise’s utility UPF Denise’s wood Jane’s wood 0 j Jane s candy Jane ’ s utility

  16. Welfare maximisation (a) (b) a Denise’s utility Denise’s utility UPF UPF e b 3 W 2 W 1 W 1 2 3 W W W c Jane ’ s utility Jane ’ s utility

  17. How do we arrive at a social preference ranking • Individuals rankings are transitive • We need a rule which allows us to convert individual rankings into a social ranking. • Majority voting • 2 prefer a to b, 2 prefer b to c, transitivity would require 2 to prefer a to c. • But 2 prefer c to a.

  18. Voting with non-transitive prefrences • With non-transitive preferences result depends on order the vote is taken in. • a compared to b then compare winner to c • a chosen in first vote • c chosen in second vote • c compared to a then compare winner to b • c chosen in first vote • b chosen in second vote

  19. Arrow’s impossibility theorem • Desirable properties of a social preference ordering. • Complete • If everyone prefers a to b, the social ranking should do the same • Social ranking of a to b should not depend on the what other alternatives are available • Dictatorship is not allowed • No rule exists which produces a ranking that always satisfies these properties

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