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Eep101/econ 125 lecture 9 Public Goods

Eep101/econ 125 lecture 9 Public Goods. David Zilberman. Overview. Original demand-1. Demand of one individual And the supply. P. D=a-bQ MC=c-dQ. D1. Q. Q1. Horizontal demand -2. Demand of one individual And the supply. P. D2H=a-Qb/2 MC=c-dQ. D1. Q2. Q1. Q.

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Eep101/econ 125 lecture 9 Public Goods

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  1. Eep101/econ 125 lecture 9Public Goods David Zilberman

  2. Overview

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

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

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

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

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

  8. 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 Dn=na-nb • The equilibrium quantity is • When there are infinite individuals the quantity demanded is equal to b/a and the demand is inelastic

  9. 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 The cost to community with n people v1s1Qno The cost to community with2n people v2s2Q2no D2n Dn v2 s2 s1 v1 o Qn Q2n

  10. 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)

  11. 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 Dn MC a D1 c Qn o

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

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

  14. Simulation a good with non rivalry and excludability

  15. Heterogeneity of preferences 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 AOQGG MC1 A Dmore C MC2 Dless G O Qc QG

  16. Heterogeneity of preferences 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) Dtotal MC1 A Dmore B C MC2 Dless G O Qc Qb

  17. Heterogeneity of preferences 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 Dtotal MC1 A Dmore B C MC2 Dless G O Qc Qb L

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

  19. 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 B A

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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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