EEP 101/Econ 125 Clubs and Congestion: Lecture 10

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EEP 101/Econ 125 Clubs and Congestion Lecture 10

• David Zilberman
• UC Berkeley

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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) /dNlt0
• d B(N,X) /dXgt0
• 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)

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ClubsOptimal size

• Socail Optimality problem
• Optimal decision rules

NMBXMCX Marginal benefits of quantity To N
members Marginal cost
NMBBenefits of the marginal memberExtra
congestion cost it inflicts -NMBN-
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Club a numerical example I

• Benefit for an individual aX-bN
• Cost cXdX2
• Optimal size Max N(aX-bN)- cX-dX2
• FOC(X) aN-c-2dX0 aN2dXc
• Hence (1) aN-2dXc alternatively
• XNa-c/2d This result is a public good result
  when N is fixed. But N is not it,it is determined
  according to

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Club a numerical example II

• FOC(N) aX-bN-2bN0
• hence X/N3b/a
• High b( congestion cost) increases optimal X/N
  ratio
• High a ( benefit of X) reduces optimal X/N ratio
  
• XN3b/a
• Positive relation between N and X
• Insert to 1 (aN-2dXc)
• (a-6db/a)Nc
• Nca/ (a-6db)
• Higher cost of the good leads to a larger club
• X3Nbc/ (a-6db)

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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.

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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.

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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