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Eep101/econ 125 lecture 9 Public Goods David Zilberman

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Overview

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Original demand-1 P Q Demand of one individual And the supply Q1 D=a-bQ MC=c-dQ D1

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Horizontal demand -2 P Q Demand of one individual And the supply Q1 D2H=a-Qb/2 MC=c-dQ D1 Q2

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Horizontal demand -large N P Q Demand of one individual And the supply Q1 DINH=a-Qb/N MC=c-dQ DH1 DHN DH2 Q2 QN

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Vertical aggregation-2 P Q Demand of two individuals And the supply Q1 D2=2a-2bQ MC=c-dQ D1 D2 Q2

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Vertical aggregation-3 P Q Demand of three individuals And the supply Q1 D3=3a-3bQ MC=c-dQ D1 D2 Q2 D3 Q3

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Vertical vs horizontal aggregation Horizontal demand lead to infinitely elastic demand at P=a. Vertical leads to infinitely in-ealstic at Q=a/b Vertical aggregation is used to find demand for public goods As the population increases the demand becomes more inelastic. The demand becomes D n =na-nb The equilibrium quantity is When there are infinite individuals the quantity demanded is equal to b/a and the demand is inelastic

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Provision of public goods Free riding- most people will wait that others will pay for the public and then they will free ride One justification for government intervention is provision of public goods Bigger communities will have larger public good provision Dn D2nD2n Qn Q2nQ2n o v1 v2 s2s2 s1s1 The cost to community with n people v 1 s 1 Qno The cost to community with2n people v 2 s 2 Q 2 no

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Provision mechanism Public provision by taxes Donations, fund raising( nature conservancy) Volunteer activity( duck unlimited,Siera club) Tax deduction-for contribution to public good generating organizations Advertisement and naming (TV,concert hall) Special institutions- The church Army Art patron (giving back to the community)

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Non rivalry with excludability If access to a good with non rivalry is possible it can be provided privately First by a monopoly- the entry fee aoc will capture all the surplus but outcome is efficient MC Dn D1 Qn a o c

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Alternative mechanism - gov’t provision fee cover costs Fee in the area OMQn/N Consumer surplus SMO MC Dn D1 Qn a O c M S

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A third mechanism- concessionaire earns competitive profit Fee in the area RMQnO/N Consumer surplus SMR Producers surplus RMO MC Dn D1 Qn a O c M S R

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Simulation a good with non rivalry and excludability

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Heterogeneity of preferences Dless Dmore MC1 MC2 G A and C optimal outcomes when only buyers that like the product more intensively are purchasing tickets. The price of ticket under monopoly are AOQcC and AOQ G G C A Qc O QGQG

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Heterogeneity of preferences Dless Dmore Dtotal MC1 MC2 G B G and B optimal outcomes In case of public good if marginal cost are high the benefits of the less interested group are important for determining the optimal outcome (Point G) C A Qc O Qb

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Heterogeneity of preferences Dless Dmore Dtotal MC1 MC2 G B In case of excludability Monopoly will provide optimal outcome at G but will charge AGLO as entry fee so that half the population will be excluded IN case of MC1 the monopoly will offer Qc C A Qc O Qb L

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Example Two equal sized groups Dmore =20-X Dless -10-X Joint demand P =30-2X for X X>10

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Case 1: MC=.5X What is Optimal X* Try 30-2X=.5X (point A) X=12 is not feasible Try 20-X (point B) =.5X socially optimal X=20/1.5=13.33 Fee by monopoly 26.66*13.33/2=311 A B

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Case 2 :MC=2X To find optimal X solve 30-2X=2X Optimal X=7.5 Benfits for people who like the product (20+20-7.5)*7.5/2=121.75 People who like less 12.5*7.5/2=46.675 Monopoly ignores second group. solves 20-X=X Optimal policy monopoly for the rich X=6.666 Fee $111 Alternative 1 regulated concessionaire providing 7.5 units for 46.675-income 93.35 Cost 56.25 Alternative 2 pay equals to cost divided by buyers

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Excludability with heterogeneity Differentiated provision- people pay different fees for different products Exclusive vs public beach Hunting licenses Different housing accommodations in national parks Allow to raise fund and pay and address equity considerations

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public good when part of the public does not care 2 groups-one does not care for D1=10-X D2=0 MC=X Should government provide public good? In this case the groups that like the product may provide it through collective action-clubs Optimal X=5 Costs 25/2= 12.5/N will be paid by users

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Clubs:Optimal size Benefits depend on amenity size X and number of users N B(N,X) Cost increases with X Optimality problem Optimal decision rules NMB=MC Marginal benefits of size = Marginal cost of congestion

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Case 2 MC=2X 30-2X=2X Optimal X=7.5 Benfits for people who like the product (20+20- 7.5)*7.5/2=178.125 Peole who like less 12.5*7.5/2=46.675 Optimal policy monopoly for the rich X=6.666 Case 3 Dmore 30-X MC=4X Optimal policy in X=8 Monopoly price to more 52*8/2=208 Monopoly price to less 12*8/2=48 In this case the monopoly will solve 30-X=4X X=6 and charge 54*6/2=162 Which means under provision Of public good

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