Unformatted text preview: EEP 101/ECON 125
EEP
Lecture 9:
Clubs and Congestion:
David Zilberman
UC Berkeley Various T ypes of Goods
Excludable Nonexcludable Rival
goods Private goods
(tomatoes) Common goods
(common pool
resources) fish Nonrival
goods Club goods
(cable TV) Public goods (national
defense) Public Goods—Main Results
Public Markets underprovide public goods
Markets
because of the free rider problem
because Need alternative mechanisms Taxes
Collective action
Privatizing the gain from giving Club Goods—Under
Alternative Assumptions
Alternative
Without
congestion
Homogenous
agents With
congestion Determine Q
monopoly, cost
recovery, concession
leads to optimality Need to determine
Q and N Heterogeneous Monopoly may be
suboptimal
agents Optimal clubs of
different sizes Club Goods with Homogenous
Agents and No Congestion
Agents A
G H E
B D2
D1 O C Club Goods with Heterogeneous
Agents and No Congestion
Agents A Ds B O C D2L
D1L Case with two users with large
Willingness to Pay (WTP) (D1L) and
a user with small WTP (Ds)
Optimal quantity OC
Entry fee under monopoly OCBA. It
cannot be paid by individuals with
small WTP
Outcome is suboptimal Clubs and Congestion
Clubs Clubs—organizations that form to provide excludable goods
Clubs—organizations
with
with Nonrivalry
Nonrivalry Congestion—utility declines with number of users B(N, X) Benefits depend on amenity size X and number of
B(N,
users N. d B(N, X) /dN < 0 d B(N, X) /dX > 0 c(X) Cost increases with X
c(X) If costs are shared, a member choice is
If MAX B(N, X)  c(X)/N which is equivalent to Max N * B(N, X)  c(X) Clubs: Optimal Size (N and X)
Clubs: Social optimality problem
MAX
NB( N ,Ê ) − χ( Ξ )
X
X, N Optimal decision rules N ∂Β( Ν, Ξ ) ∂χ( Ξ )
−
=0
∂Ξ
∂Ξ
Ν∂Β( Ν,⊇ )
Ξ
Β( Ν,⊇ ) +
Ξ
=0
∂Ν N * MBX = MCX
Marginal benefits of
quantity to N members
= marginal cost
B benefits of the marginal
member = extra
congestion cost it inflicts =
 N * MBN* Congestion Costs
Congestion When there are congestion externalities,
When
each user inflicts NdB(N, X)/dN of extra
cost on the other users.
cost If B(N, X) = aX  bX2  eN  fN2  cX  dX2 ,
eN
cX
the marginal congestion cost of each
individual is e + 2fN
individual Club: Numerical Example I
Club: Benefit for an individual aX  bX2  eN  fN2
eN
Cost cX + dX2
Solve Max N(aX  bX2  eN  fN2)  cX  dX2
eN
Find optimal X for every N and then find the
Find
optimal N by comparison FOC(X) N(a  2bX)  c  2dX = 0. Hence
FOC(X) X(N) = (Na  c)/2(Nb + d) This result is a public good when N is fixed, but
This
N can be changed
can Special case—B(X, N) = 10X  2X2  .2N  .05N2
Special
.2N
and c(X) = X + X2 Max N(10X  2X2  .2N  .05N2)  X  X2
.2N Given N, the FOC with respect to X is
Given
10N  4NX  1  2X = 0
10N For N = 1, the optimal condition is 9 = 6X
X = 1.5
1.5 Benefits in this case, 15  2 * 2.25  .2  05
Benefits
1.5  2.25 = 15  4.5  .25  3.75 = 15  8.5 =
6.5
6.5 Special case—B(X, N) = 10X  2X2  .2N
Special
 .05N2 and c(X) = X + X2
.05N Max N(10X  2X2  .2N  .05N2 )  X  X2
.2N Given N, the FOC with respect to X is
Given
10N  4NX  1  2X = 0
10N For N = 2, the optimal condition is
For
20  8X = 1  2X, 19  10X, X = 1.9
1.9 Benefits in this case: 2(19  2 * 3.61  .2
Benefits
 05) 1.9  3.61 = 16.85
16.85 Club: Numerical Example II
Club: Since N is a discrete variable, you solve the problem for N
Since
= 1, 2, large number and find the maximum B(X, N) = 10X  2X2  .1N  .05N2 and c(X) = X + X2 , the
.1N
solution
solution Optimal number
of club members
is 8 Club: Numerical Example III
Club: B(X, N) = aX  bX2  eN  fN2 c(X) = cX + dX2
c(X)
eN
B(X, N) = 10X  2X2  .2N  .05N2 and c(X) = X + X2
.2N
Consider now cases with
a = 12, N* = 10 D = 2, e = .3, N* = 7
Optimal club size
increases with benefits
of good and declines
with
congestion costs Nonexcludable Goods with Nonrivalry:
oods
Finance for Efficiency and Equity Progressive income tax Highway: charge for less congested lanes Recreation: distribute right for exclusive
Recreation: development in exchange for public facilities
development Housing: require lowincome housing as a
Housing:
condition of development right
condition Transportation: tax pollution and congestion for
Transportation:
public transport
public Education: charge the rich to finance the
Education:
talented poor Freedom to Choose
Freedom Clubs are established to accommodate
Clubs
people with different preferences.
people Clubs with members with a high degree of
Clubs
preference for goods and high aversion to
congestion will charge a high membership
fee and be exclusive.
fee Municipalities are also clubs. Different communities have different
Different
combinations of services and taxes.
combinations People Choose with Their Feet
People People will relocate to locations that provide them
People with the optimal combination of environmental
amenities, employment, congestion, and taxes.
amenities,
Some people who prefer a high degree of services
Some
with high taxes will join the appropriate community.
with
Therefore, uniform environmental policies have a
Therefore,
disadvantage and, when possible, communities will
be allowed to establish their own standards.
But some environmental choices have implications
But
that spill over nationally and globally.
Others impact future generations. Environmentalism & Federalism
Environmentalism The theory of public goods and externality are useful
The
to determine what type of policies should be
determined by global, federal, and municipal
governments. The federal government sometimes aims to establish
The
minimum standards that apply to all populations and
take into account a future generation. Groups that have stronger preference than the
Groups
average may establish clubs to pursue their
objectives. The legal system is crucial in dividing responsibilities
The
between various levels of government.
between ...
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 Spring '09
 ZELBERMAN
 Public Good, congestion, Club Goods

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