EEP101_lecture9 - EEP 101/ECON 125 EEP Lecture 9: Clubs and...

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Unformatted text preview: EEP 101/ECON 125 EEP Lecture 9: Clubs and Congestion: David Zilberman UC Berkeley Various T ypes of Goods Excludable Non-excludable Rival goods Private goods (tomatoes) Common goods (common pool resources) fish Non-rival 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 Non-rivalry Non-rivalry 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 low-income 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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