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Lecture%2017%20Public%20Goods%201 - Public Goods Public...

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1 Public Goods Public Good: Excludability: (knowledge, clean air, etc.) Commodity for which the use of a unit of the good buy one agent does not preclude its use by other agents Others cannot be excluded from consumption (clean air, national defense) An Economy with a Public Good Two agents : i = 1, 2 They consume: a public good: G Preferences: U i (X i , G) Endowments: ω 1 and ω 2 of the private good The public good G has to be produced Technology: Linear PPF We can normalize units so that one unit of the private good yields one unit of public good a private good: X i An Economy with a Public Good The Individuals Problem: or, by substituting for X i from (i): ) , X i ( U i i , X i Max B G A G ω ω ω + G ) , ( U Max i ω ω ω ω ω B G A G i G i x i G + ω i x i G i ω X = + s.t. (i) 0 , 0 x ω i G i (ii) ω ω i x i G 0 s.t.
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2 consumption of good 1 by i A Graphical Analysis Nice features of the Edgeworth box: 1. Any point in the Edgeworth Box is a possible distribution of goods given endowments good 2 j good 1 i consumption
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