Externality-Public Good

Externality-Public Good - Externalities and Public Goods...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Externalities and Public Goods Econ 210C UCSB May 23, 2011
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Externalities An externality is present if the well-being of a consumer or the production possibilities of a producer is directly affected by actions of another agent (a consumer or a producer). Example (Coase, 1960): A farmer and a rancher had adjoining properties. There was no fence. The rancher’s cattle could wander over to the farmer’s property and eat some the his wheat. The more cattle there were, the more wheat was eaten. Profit Functions: Π f ( w , c ) for the farmer and Π r ( w , c ) for the rancher, where w denotes a generic quantity of wheat and c the number of cattle. Assume Π f ( w , c ) c < 0 and Π r ( w , c ) w > 0. (1) Econ 210C UCSB Paper
Background image of page 2
Econ 210C UCSB Paper
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Econ 210C UCSB Paper
Background image of page 4
Non-Cooperative Solution: Let ( c * , w * ) be a Nash equilibrium such that w * > 0 and c * > 0. Then, ( c * , w * ) satisfies Π f ( w , c ) w = 0 and Π r ( w , c ) c = 0. (2) Pareto Optimal Solution: A PO solution can be found by solving max [ λ f Π f ( w , c ) + λ r Π r ( w , c )] for some choice λ = ( λ f , λ r ) ∈ < 2 + . At the interior solution, λ f Π f ( w , c ) w + λ r Π r ( w , c ) w = 0 λ f Π f ( w , c ) c + λ r Π r ( w , c ) c = 0. (3) By (1), (2), and (3), Nash equilibrium is not Pareto optimal. Econ 210C UCSB Paper
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Econ 210C UCSB Paper
Background image of page 6
A Simple Model with Externality E = { X i , u i , ω i } 2 i = 1 where X i = < 2 + and ω i = ( ω ix , ω im ) , u i ( x i , m i , h ) = φ i ( x i , h ) + m i h ∈ < + is a level of an activity consumer 1 may choose. There is no market for externality (i.e. for activity h ). Given h ∈ < + and market prices p x for the consumption good, consumer i ’s utility maximization problem is max φ i ( x i , h ) + m i s . t . p x x i + m i = p x ω ix + ω im where v i ( · ) is consumer i ’s indirect utility function. Since u i ( x , m i , h ) is quasi-linear, the consumer’s indirect utility function is also quasi-linnear v i ( p , w i , h ) = ψ i ( p , h ) + w i . Econ 210C UCSB Paper
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Consumer 1’s Optimal Activity Level: max h 0 ψ 1 ( p , h ) . At the optimal level, ψ 0 1 ( p , h ) 0 and h ψ 0 1 ( p , h ) = 0. (4) Pareto Optimal Activity Level: Due to quasi-linearity of consumers’ utility functions, the Pareto optimal activity level is determined by max h 0 [ φ 1 ( p , h ) + ψ 2 ( p , h )] .
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/26/2011 for the course ECON 210C taught by Professor Qin during the Fall '09 term at UCSB.

Page1 / 21

Externality-Public Good - Externalities and Public Goods...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online