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  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*MB X =MC X Marginal benefits of quantity To N members =Marginal cost N*MB=Benefits of the marginal member=Extra congestion cost it inflicts= -N*MB N-

Club a numerical example I  Benefit for an individual aX-bX 2 -eN-fN 2  Cost cX+dX 2  Solve Max N(aX-bX 2 -eN-fN 2 )- cX-dX 2  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-2X 2 -N-.1N 2 and c(X)=X+X 2 the solution Optimal number of club members is 8

Club a numerical example III  B(X,N)= aX-bX 2 -eN-fN 2 c(X)= cX+dX 2  B(X,N)=10X-2X 2 -N-.1N 2 and c(X,)= X+X 2  Consider now cases with a=12 e=3 a=12 optimal N=10 E=3.optimal N=7 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  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 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  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