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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- 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

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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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