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GWLecture16

# GWLecture16 - Part IIa Paper 1 General Equilibrium and...

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1 Part IIa: Paper 1 General Equilibrium and Welfare Economics Dr Sönje Reiche

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2 Outline Externalities Pigouvian Taxes Coase Theorem Information problem Second best policies Common Property Resources (Nothing on imperfect competition)
3 Efficiency and Externalities ( 29 B A A A z x z z x u A A , , max , A A A e pz x = + Consider a two person, two good economy Individual A’s maximisation problem, taking B’s choice of x and z as given: ( 29 λ = B A A A x z z x u A , , ( 29 ( 29 p z z x u z z x u B A A A x B A A A z A A = , , , , Assume that good z is produced by using good x: 1 unit of z requires p units of x. ( 29 λ p z z x u B A A A z A = , , Marginal utility w.r.t x A

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4 Efficiency and Externalities ( 29 B B B z x z x u B B , max , B B B e pz x = + Individual B’s problem: ( 29 ( 29 p z x u z x u B B B x B B B z B B = , , subject to: B A MRS MRS = … where is the inefficiency?
5 ( 29 B B B z z x x z x u B A B A , max , , , B A B A B A e e pz pz x x + = + + + Pareto efficiency: subject to: ( 29 κ λ = B A A A x z z x u A , , ( 29 p z z x u B A A A z A κ λ = , , ( 29 κ = B B B x z x u B , ( 29 ( 29 p z z x u z x u B A A A z B B B z B B κ λ = + , , , ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 B A A A x B A A A z B B B x B B B z B A A A x B A A A z z z x u z z x u z x u z x u z z x u z z x u A B B B A A , , , , , , , , , , + = MRS for A (Social) MRS for B ( 29 A B A A A u z z x u = , , f.o.c.:

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6 Efficiency and Externalities Social marginal benefit differs from private marginal benefit, and so social MRS differs from private MRS Individuals set private MRS equal to price, so inefficiency
7 Efficiency and Externalities Z B MC, MB MC MB B SMB * B z B z ( 29 B A A A z z z x u B , , in partial equilibrium, such that ( 29 ( 29 1 , , , = = B B B x B A A A x z x u z z x u B A

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8 Pigouvian Taxes ( 29 ( 29 ( 29 ( 29 p z z x u z z x u z x u z x u B A A A x B A A A z B B B x B B B z A B B B = + , , , , , , Optimality: ( 29 ( 29 p z x u z x u B B B x B B B z B B = , ,
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