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

EEP 101/Econ 125 Clubs and Congestion: Lecture 10

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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

- 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

- 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

- 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

- 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

- 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

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