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# EEP 101/Econ 125 Clubs and Congestion: Lecture 10 - PowerPoint PPT Presentation

EEP 101/Econ 125 Clubs and Congestion: Lecture 10. David Zilberman UC Berkeley. Clubs and congestion. Clubs- organizations that form to provide excludable goods with Non rivalry Congestion- utility declines with number of users

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### EEP 101/Econ 125 Clubs and Congestion: Lecture 10

David Zilberman

UC Berkeley

• Clubs- organizations that form to provide excludable goods with

• Non rivalry

• Congestion- utility declines with number of users

• B(N,X) Benefits depend on amenity size X and number of users N.

• d B(N,X) /dN<0

• d B(N,X) /dX>0

• c(X) Cost increases with X

• If costs are shared a member choice is

• MAX B(N,X)-c(X)/N which is equivalent to

• Max N* B(N,X)-c(X)

• Socail Optimality problem

• Optimal decision rules

N*MBX=MCX

Marginal benefits of quantity

To N members

=Marginal cost

N*MB=Benefits of the marginal member=Extra congestion cost it inflicts= -N*MBN-

• Benefit for an individual aX-bX2-eN-fN2

• Cost cX+dX2

• Solve Max N(aX-bX2-eN-fN2)- cX-dX2

• Find optimal X for every N and then find the optimal N by comparison

• FOC(X) N(a-2bX)-c-2dX=0 Hence

• X(N)=(Na-c)/2(Nb+d)

• This result is a public good result when N is fixed. But N can be changed

• Since N is a discrete variable you solve the problem for N=1,2 , large number and find the maximum

• B(X,N)=10X-2X2-N-.1N2 and c(X)=X+X2 the solution

Optimal number of

club members

is 8

• B(X,N)= aX-bX2-eN-fN2c(X)= cX+dX2

• B(X,N)=10X-2X2-N-.1N2 and c(X,)= X+X2

• Consider now cases with a=12 e=3

E=3.optimal N=7

a=12 optimal N=10

Optimal club size

increases with benefits

of good and declines with

congestion costs

• Progressive income tax

• Highway- congestion is a cost- charge for less congested lanes

• Recreation: distribute right for exclusive development in exchange for public facilities

• Housing: require low income housing as a condition of development right

• Transportation: tax pollution and congestion for public transport

• Education: charge the rich to finance the talented poor

Freedom to Choose and equity

• Clubs are established to accommodate people with different preferences.

• Clubs with members with a high degree of preference for goods and high aversion to congestion, will charge a high membership fee and be exclusive.

• Municipalities are also clubs.

• Different communities have different combinations of services and taxes.

People choose with their feet. and equity

• People will relocate to locations that provide them with the optimal combination of environmental amenities, employment, congestion, and taxes.

• Some people who prefer a high degree of services with high taxes, will join the appropriate community.

• Therefore, uniform environmental policies have a disadvantage and when possible, communities will be allowed to establish their own standards.

• But some environmental choices have implications that spill over nationally and globally.

• Others impact future generations.

Environmentalism & Federalism and equity

• The theory of public goods and externality are useful to determine what type of policies should be determined by global, federal, and municipal governments.

• The federal government sometimes aims to establish minimum standards that apply to all populations and take into account a future generation.

• Groups that have stronger preference than the average, may establish clubs to pursue their objectives.

• The legal system is crucial in dividing responsibilities between various levels of government