Eep 101 econ 125 clubs and congestion lecture 10
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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

EEP 101/Econ 125 Clubs and Congestion: Lecture 10

David Zilberman

UC Berkeley


Clubs and congestion
Clubs and congestion

  • 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)


Clubs optimal size
Clubs:Optimal size

  • 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-


Club a numerical example i
Club a numerical example I

  • 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


Club a numerical example ii
Club a numerical example II

  • 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


Club a numerical example iii
Club a numerical example III

  • 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


Nonexcludable goods with nonrivalry finance for efficiency and equity
Nonexcludable goods with nonrivalry: Finance for efficiency and equity

  • 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
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
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
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


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