EEP 101/Econ 125 Clubs and Congestion: Lecture 10

1. EEP 101/Econ 125 Clubs and Congestion: Lecture 10 David Zilberman UC Berkeley

2. 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)

3. 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-

4. 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

5. 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

6. 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

7. 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

8. 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.

9. 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.

10. 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