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Unformatted text preview: EEP 101/Econ 125 EEP Clubs and Congestion: Lecture 9 Lecture
David Zilberman UC Berkeley Various types of goods Various
excludable Rival goods Private goods ( tomaotes) Non excludable Common goods ( common pool resources) Fish Public good (National defense) Non rival goods Club good (cable TV) Public good- main results Public Market under provide public goods Market
because of the free rider problem because Need alternative mechanism Taxes Collective action Privatizing the gain from giving Club goods-under alternative assumptions assumptions
Without congestion Homogenous agents With congestion
Determine Q Need to determine Monopoly, Cost Q and N recovery, Concession lead to optimality Monopoly may be suboptimal Optimal clubs of different sizes heterogeneous agents Club with homogenous agents and no congestion agents A G E B O C H D2 D1 Club good heterogeneous agents no congestion agents
Case with 2 users with large Willingness to Pay (D1L) and a user with small WTP (Ds) Optimal quantity OC Entry fee under monopoly OCBA It can not be paid by individual with small WTP Outcome is suboptimal Ds O B C D2L D1L A Clubs and congestion Clubs Clubs- organizations that form to provide excludable goods with Non rivalry Non Congestion- utility declines with number of users B(N,X) Benefits depend on amenity size X and number of users B(N,X)
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) Social Optimality problem
MAX X, N NB( N .X ) − χ( Ξ ) Clubs:Optimal size (N and X) Clubs:Optimal 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- Club a numerical example I Club Benefit for an individual aX-bX2-eN-fN2 Cost cX+dX2 Solve Max N(aX-bX2-eN-fN2)- cX-dX2 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 result when N is fixed. But N can be changed fixed. Special case B(X,N)=10X-2X2-.2N-.05N2 Special and c(X)=X+X2 and Max N(10X-2X2-.2N-.05N2)-X-X2 Given N the FOC with respect to X is Given 10N-4NX-1-2X=0 For N=1 the optimal condition is 9=6X X=1.5 For X=1.5 Benefits in this case15-2*2.25-.2-05-1.5-2.25 =15-4.5-.25-3.75=15-8.5=6.5 Special case B(X,N)=10X-2X2-.2N-.05N2 Special and c(X)=X+X2 and Max N(10X-2X2-.2N-.05N2)-X-X2 Given N the FOC with respect to X is Given 10N-4NX-1-2X=0 For N=2 the optimal condition is For 20-8X=1-2X 19-10X X=1.9 20-8X=1-2X X=1.9 Benefits in this case 2(19-2*3.61-.2 -05) -1.9 Benefits
-3.61=16.85 -3.61= Club a numerical example II Club Since N is a discrete variable you solve the problem for Since
N=1,2 , large number and find the maximum B(X,N)=10X-2X2-.1N-.05N2 and c(X)=X+X2 the solution the Optimal number of club members is 8 Club a numerical example III Club B(X,N)= aX-bX2-eN-fN2 c(X)= cX+dX2 c(X)= B(X,N)=10X-2X2-.2N-.05N2 and c(X,)= X+X2 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 Progressive income tax Highway- charge for less congested lanes Recreation: distribute right for exclusive Recreation: Nonexcludable goods with nonrivalry: Finance for efficiency and equity Finance 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. membership Municipalities are also clubs. Different communities have different Different combinations of services and taxes. combinations People will relocate to locations that provide them People People choose with their feet. 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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