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EEP 101/Econ 125 Clubs and Congestion: Lecture 10

This lecture explores the formation of clubs for providing excludable goods efficiently. It discusses the impact of congestion on utility, optimal club size, and decision rules balancing costs and benefits. The text provides numerical examples and discusses the implications of personalized club choices on societal welfare. The role of clubs in accommodating diverse preferences and the implications of varying environmental policies on communities are also examined. Additionally, it delves into the intersection of environmentalism, federalism, and the legal system in determining governance and policy responsibilities.

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EEP 101/Econ 125 Clubs and Congestion: Lecture 10

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  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-bN • Cost cX+dX2 • Optimal size Max N(aX-bN)- cX-dX2 • FOC(X) aN-c-2dX=0 aN=2dX+c • Hence (1) aN-2dX=c alternatively • X=Na-c/2d This result is a public good result when N is fixed. But N is not it,it is determined according to

  5. Club a numerical example II • FOC(N) aX-bN-2bN=0 • hence X/N=3b/a • High b( congestion cost) increases optimal X/N ratio • High a ( benefit of X) reduces optimal X/N ratio • X=N3b/a • Positive relation between N and X • Insert to 1 (aN-2dX=c) • (a-6db/a)N=c • N=ca/ (a-6db) • Higher cost of the good leads to a larger club • X=3Nbc/ (a-6db)

  6. 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.

  7. 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.

  8. 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

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