PUBLI C GOODS 1 Hillman 2009: Chapter 3 Public goods Public goods - PowerPoint PPT Presentation

Hillman 2009: Chapter 3 Public goods The public good game with divided money Each individual has a budget constraint    10 x g i 1, 2. i i When the game is against one other person   G g g . 1 2 Example of a formula that determines personal total benefits B i       3 2 3 2( ) 1, 2. B x G x g g i i i i 1 2 Person 2 Person 2 does contributes not contribute Person 1 contributes 40, 40 20,50 Person 1 does not 50, 20 30, 30 contribute 23

Hillman 2009: Chapter 3 Public goods Total benefit from a personal contribution of one dollar = 4 Max B=B 1 +B 2 : all money for the public good The dominant strategy is not to contribute to the public good Cooperation often occurs except in the final round People appear to anticipate punishment, should they cease to cooperate – except the last time 24

Hillman 2009: Chapter 3 Public goods Trust and norms of conduct People often begin by trusting others to reciprocate People are willing to punish others who did not cooperate, even if in the act of punishment they themselves incur a loss Economics students and cooperation Economics students tend to cooperate less Economics students may better understand the logical consequence of common knowledge 25

Hillman 2009: Chapter 3 Public goods Cooperation as expressive Expressive behavior by economics students People confirm their identity The sums of money are small How significant is the experimental evidence on public goods for public finance and public policy? Even if people cooperate in experiments, governments could not rely on voluntary payments to finance public goods If contributions were voluntary, there would be no tax evasion. 26

Hillman 2009: Chapter 3 Public goods Sequential voluntary-financing public-good games When valuations of public goods differ, do high-valuation or low- valuation beneficiaries contribute first? What behavior do we expect when a discrete public good requires a minimal level of contributions before providing benefits? 27

Hillman 2009: Chapter 3 Public goods C. W eakest-link and volunteer-type public goods For a public good described by the prisoners’ dilemma: n   G g i  i 1 For weakest-link public goods:         min , , ,..., .... G g g g g G G G G 1 2, 3 n 1 2 3 n The lowest standard determines the overall standard  A wall that protects homes against sea water on a circular island  Safety in a neighborhood  The quality of a road  The effectiveness of defense  The time taken for a group to complete a hike 28

Hillman 2009: Chapter 3 Public goods Strategic behavior for weakest-link public goods Person 2 does not Person 2 contribute contributes 24, 24 4, 10 Person 1 contributes (0.3).(0.3)= 0.09 (0.3).(0.7)= 0.21 Person 1 does not 10,4 10, 10 contribute (0.7).(0.3)= 0.21 (0.7).(0.7)= 0.49 Derivation of the mixed-strategy equilibrium Utility (not contribute) = 10 Utility (contribute) = P.24 + (1 – P).4 Equate and solve: P = 0.3 29

Hillman 2009: Chapter 3 Public goods 10,10 NO Person 2 decides NO YES 4, 10 Person 1 4, 10 decides NO YES Person 2 decides YES 24, 24 Sequential decisions for weakest-link public goods solve the coordination problem Cheap talk  A declaration of intent on which it is costless to renege  In coordination games such as supply of weakest-link public goods, “cheap talk” provides valuable communication  It is in the self-interest of people who declare that they will contribute to the public good to actually do so 30

Hillman 2009: Chapter 3 Public goods A role for government?  Free riding is impossible: unless everyone pays, the public good is not provided  Paying for a weakest-link public good is therefore like paying for a private good  Every person needs to pay and wants to pay – provided everyone else pays  Taxation and public spending are not necessary because everyone has an interest in participating to provide the efficient outcome 31

Hillman 2009: Chapter 3 Public goods Volunteer-type public goods         G max g g , , g ,..., g G G G .... G 1 2, 3 n 1 2 3 n  Help to move a disabled car  Remove a rock from a road  A broken bottle on a path  A story from the Netherlands: a boy who placed his finger in a hole in a dyke  Passengers lining up to board a plane may notice that a person is acting suspiciously 32

Hillman 2009: Chapter 3 Public goods Who provides the public good? The game of chicken Person 2 Person 2 does contributes not contribute 10,10 10,12 Person 1 (0.8).(0.8)= (0.8).(0.2)= contributes 0.64 0.16 Person 1 does not 12,10 2,2 contribute (0.2).(0.8)= (0.2).(0.2)= 0.16 0.04 There is no dominant strategy The two Nash equilibria are efficient For the mixed strategy, P= 0.8 33

Hillman 2009: Chapter 3 Public goods 2, 2 NO Person 2 decides NO YES 12, 10 Person 1 10, 12 decides NO YES Person 2 decides YES 10,10 Sequential decisions for volunteer type public goods The first person to decide imposes the cost of supply on the second person Larger populations and sequential decisions: each person can choose to rely on the next person, if there is a next person 34

Hillman 2009: Chapter 3 Public goods Social norms and volunteer public goods  Personal contributions can be based on convention, as within a household  Within broader society, can we rely on similar conventions?  Social norms influence personal behavior, through our expectations about how we feel we should act in different situations  A society in which the social norm is to take personal responsibility has more volunteer-type public goods The role for government? Since decisions are personal and voluntary, there is no role for government – except perhaps through education Example: Personal freedom as a voluntarily privately supplied public good 35

Hillman 2009: Chapter 3 Public goods D. National security Special characteristic of national security as a public good The effectiveness of defense spending depends spending of potential adversaries Spending on defense as a prisoners’ dilemma Country 2 does Country 2 not spend on spends on military military preparedness preparedness Country 1 does not spend on military 3, 3 1, 4 preparedness Country 1 spends on 4, 1 2, 2 military preparedness 36

Hillman 2009: Chapter 3 Public goods International treaties and free-riding problems between allies Free riding within a country Peace as a public good: A strong country acting ethically provides a pure public good, in sustaining peace in an otherwise anarchic world. Democracies and conflict  In autocracies, the ruler personally enjoys the benefits of conquest and imposes the costs on the people  In democracies, the benefits of conquest are not personal but the costs are personal, so voters oppose initiation of war. 37

Hillman 2009: Chapter 3 Public goods Defense against terror and asymmetric warfare What is asymmetric warfare? What are the costs of terror for the population of intended victims? Income and terror: Is economic derivation the reason for terror? Definition: A supreme-value objective is an objective that is sought without the possibility of compromise. Is deterrence effective in the face of supreme-value terror? Are there other solutions for defense against terror? 38

Hillman 2009: Chapter 3 Public goods Penalties on family assets Terrorists’ decision Commit Victims’ decision No terror terrorist acts Family assets are 2, 3 3, 1 appropriated No penalty on 1, 4 4, 2 terrorists’ families  Neither the victims of terror nor the terrorists want the terrorists’ families to be penalized  The victims have no dominant strategy The dominant strategy of the terrorists is to commit acts of terror 39

Hillman 2009: Chapter 3 Public goods Sequential decisions  The terrorists decide first  (3, 1) and (1, 4) are not possible equilibria  Terrorists are better off at (2, 3) than at (4, 2)  Deterrence has been ineffective 4, 2 4,3 NO 1 Victim decides Alternative YES 3, 1 NO terrorist Terrorist preference decides 1, 4 NO YES 2 Victim decides YES 2, 3 2,2 Alternative preferences: Intending terrorists prefer (no terror, no penalty) to (terror and penalty on the family) and deterrence is effective By choosing first, the terror organization determines the outcome 40

Hillman 2009: Chapter 3 Public goods Repeated “games” between terrorists and victims: If the penalty is not imposed, there is no credible deterrent when intending terrorists prefer the (no terror, no penalty) solution Moral dilemmas for intended victims when the identity of the terrorists is not known with certainty  Profiling  Unintended collective punishment Social and political divisions because of the moral dilemmas 41

Hillman 2009: Chapter 3 Public goods 3 .2 I NFORMATI ON AND PUBLI C GOODS The public-good information problem Weakest-link public goods  A coordination problem  No one wants to free ride Volunteer-type public goods  Social norms and personal values determine behavior  Free riding is efficient Public goods of the prisoner’s dilemma  There is a role for government because of free riding  When people seek to free ride, government has the advantage of being able to legally coerce payment through taxation 42

Hillman 2009: Chapter 3 Public goods A. Can governm ents solve the inform ation problem ? Can governments solve the public-good information problem and overcome the free-riding incentives that prevent efficient supply of prisoners’- dilemma type public goods? Another form of the same question: Can government replicate the efficient Lindahl consensus when MB’s are private information of individuals? The problem is more complex than was illustrated in the public- good prisoners’ dilemma 43

Hillman 2009: Chapter 3 Public goods Price and valuation of the public good P = MC = AC ∑ MB O Quantity G E Choosing the efficient quantity to supply Can government determine G E ? The government replicates the efficient Lindahl solution through taxes if   T MB , i 1,..., n i i   MB MC i i ∑ MB is required information for the government 44

Hillman 2009: Chapter 3 Public goods Governments wishing to levy taxes to finance public goods confront the same asymmetric information problem that impedes efficient voluntary payments for public goods We shall consider three solutions to the public-good information problem: 1. A mechanism designed to elicit truthful responses 2. User prices 3. Locational choice 45

Hillman 2009: Chapter 3 Public goods B. The Clarke tax and truthful self-reporting People could be asked their MB with assurance that reported personal MB will not be used to determine personal payments for financing the public good The incentive is then to overstate benefit Illusion: “governments” and not taxpayers are paying Can incentives be provided for people to report their benefits from public goods voluntarily and truthfully ? 46

Hillman 2009: Chapter 3 Public goods The Clarke tax Person Person 1 Person 2 3 100 70 -80 Tax=10 Tax=0 Tax=0 W = B – C > 0 The government does not know the personal benefits and costs There is asymmetric information: only the three people know their own personal benefits or losses 47

Hillman 2009: Chapter 3 Public goods Rules for the Clarke tax o People pay a tax for being decisive o The amount of the tax payment is equal to the net loss imposed on all other people as a consequence of being decisive o The tax revenue is not used to finance the project nor to benefits the persons involved in other ways 48

Hillman 2009: Chapter 3 Public goods  The impossibility of gain from misrepresentation: Nothing that people say about their own valuations of benefits or costs affects the value of the Clarke tax that a person pays  The Clarke tax results in Nash equilibrium: The dominant strategy is to reveal truthfully personal benefit or loss from the public good and to pay the Clarke tax  Why cannot the revenue benefit the people involved? 49

Hillman 2009: Chapter 3 Public goods A case where no one is decisive Person 1 Person 2 Person 3 Person 4 20 20 20 -30 Tax=0 Tax=0 Tax=0 Tax=0 The tax is zero for everybody because no one’s participation in the evaluation of benefit and cost is decisive in changing the outcome 50

Hillman 2009: Chapter 3 Public goods The Clarke tax with two projects Person 1 Person 2 Person 3 Project A 70 80 20 Project B 30 50 80 Clarke tax Tax=30 Tax=20 Tax=0 51

Hillman 2009: Chapter 3 Public goods No government ever appears to have used the Clarke tax as a means of solving the public-good asymmetric-information problem Why is the Clarke tax not used?  Complexity?  Unfairness: the taxes do not finance the public good  Political reasons: the uncertainty of not knowing beforehand how the Clarke mechanism will determine tax obligations for different people 52

Hillman 2009: Chapter 3 Public goods C. User prices Apply the benefit principle and exclude people who do not pay to create a market for use Definition: The benefit principle (a normative proposition) People who benefit should pay People who do not benefit should not have to pay Efficient Lindahl prices do not exclude people from benefits of public goods (we saw that exclusion for pure public goods is inefficient) User prices differ from efficient Lindahl prices. 53

Hillman 2009: Chapter 3 Public goods If a person i voluntarily pays a user price, we know that  use MB P i i  People reveal their personal benefit by paying user prices  The efficient user price is zero, so user prices inefficiently exclude from pure public goods  User prices provide revenue to pay for public goods 54

Hillman 2009: Chapter 3 Public goods Indirect user prices  A tax on gasoline is a tax on use of roads  A tax on automobiles is a tax on the option to use a road  The user prices can be avoided by not using or owning an automobile. Subsidies and partial user prices  School fees (user prices) may cover only part of the cost of education  User prices for health care may be subsidized Two-part user prices User prices can be in two parts for fixed and variable costs Example: School administrators and teachers 55

Hillman 2009: Chapter 3 Public goods User prices and fixed costs Pure public goods have fixed costs that are independent A total fixed cost of use F per period of time can be imputed from the value of the initial investment plus interest payments and deprecation over time With n users, the average cost of use per period of time is F  AC . n 56

Hillman 2009: Chapter 3 Public goods Are self-financing user prices feasible? Definition: P use =AC is a self-financing user price AC is a rectangular hyperbola Self–financing User valuation user price v use Demand P 1 for use use P 2 AC=F/n O O n 2 n 1 Number n Number of of users users Demand for use of a The self-financing user- public facility price is equal to average cost 57

Hillman 2009: Chapter 3 Public goods  People are excluded by the user price  Without user prices, there may be no bridge or no college, because of the free-rider problem due to asymmetric information.  The self-financing user price finances availability of public goods by requiring payment for benefit 58

Hillman 2009: Chapter 3 Public goods In case A a population smaller in size than n 1 cannot self-finance the public good through user prices In case B self-financing user-prices do not exist – although with free access, W = (B - C) > 0 Valuation and cost Valuation and cost Demand H for use 1 use P 1 Demand for use AC=F/n E 2 AC J A use P 2 R Number O n 1 n 2 n Number O of users n of users Case A Case B Self-financing user prices may not exist for projects that satisfy the cost-benefit criterion W = (B - C) > 0 59

Hillman 2009: Chapter 3 Public goods Private supply Example: A bus service Valuation and cost AC Demand for use Per-unit subsidy required for Maximized profits P M private supply with no exclusion of an unregulated private supplier use P 2 MR MC=0 n M O n 2 n Number of users Private supply by a monopoly  The private profit-maximizing supplier excludes ( n - n M ) potential users  For efficient use, all n potential users should be given access at a zero price: there is then no revenue, so a subsidy from government is required 60

Hillman 2009: Chapter 3 Public goods Subsidies from government budget to private suppliers are undesirable because of principal-agent problems Governments can ask for competitive bids from private suppliers: then there are problems of incomplete contracts With government ownership:  Subsidies are avoided  There is a bureaucratic principal-agent problem, because of incentives for budget maximization of the officials in the administering government bureaucracy 61

Hillman 2009: Chapter 3 Public goods A basic question: Are user prices desirable means of resolving the public-good asymmetric-information problem? 62

Hillman 2009: Chapter 3 Public goods Social justice The normative principle of ability-to-pay. The ability of pay principle of taxation is that people should pay for public goods according to their means and without regard for personal benefit.  Under the ability to pay principle, people with higher incomes pay higher taxes  Under the benefit principle on which user prices are based, people pay the same user prices independently of income. 63

Hillman 2009: Chapter 3 Public goods Efficiency  We consider user prices because of the objective of efficiency , not social justice  We ideally want efficient Lindahl prices but Lindahl prices are not feasible: hence we turn to user prices  The case for user prices is that, in voluntarily paying, people reveal MB from public goods  Ability-to-pay taxes: people finance public goods that they do not use and so the link between personal benefit and personal payment is broken  User prices directly link voluntary personal spending to personal benefit The inefficiency of exclusion  Self-financing user prices inefficiently exclude 64

Hillman 2009: Chapter 3 Public goods Accountability  User prices provide accountability  When payment is made through user prices, people are more attentive to whether appropriate benefits have been received. User prices as an alternative to government supply  Government schools in some countries and locations fail to provide quality education  When governments provide free-access tax-financed health care, user prices paid for private health care may be the only escape from inadequacies of government supply 65

Hillman 2009: Chapter 3 Public goods Prisons and police  Prisons can be financed through user prices paid by inmates  The user prices are involuntary  Should taxpayers and citizens, as victims of crime, be obliged to pay for prisons  Competitive bidding for private supply of prisons Police protection  It is unjust or unethical to compel victims of crime to pay when government has been ineffective in enforcing the rule of law  User prices for calling on the police would also assist criminals by deterring reporting of crime. 66

Hillman 2009: Chapter 3 Public goods Diversity in application of user prices  In some countries user prices are applied extensively to solve the public-good asymmetric-information problem  In other countries, user prices are uncommon  In low-income societies, voluntary user prices are paid to substitute for absent or inadequate government supply 67

Hillman 2009: Chapter 3 Public goods D. The Tiebout locational choice m echanism Locational choice is an application of the benefit principle of taxation Does choice of location among government jurisdictions achieve efficiency, as a substitute for a competitive market in public goods? Does locational choice replicate the efficient Lindahl voluntary-payment solution for public goods? 68

Hillman 2009: Chapter 3 Public goods  The efficient Lindahl solution requires everyone in the one jurisdiction to finance pure public goods.  If people choose to finance public goods in different locations, there is inefficient duplication of supply (because a pure public good is a natural monopoly).  Still, locational choice is the efficient second-best solution, given the asymmetric information problem that prevents the efficient solution. 69

Hillman 2009: Chapter 3 Public goods Tiebout and Samuelson on spontaneous and imposed order The Tiebout locational mechanism (1956) is named after Charles Tiebout (1924–68) Tiebout replied to Paul Samuelson (1954, 1955). Samuel on proposed:  ∑ MB=MC for efficient public good supply could not be achieved through voluntary payment for public goods because people would not pay according to their true MB .  Imposed order was therefore required for public goods through supply decisions of centralized government agencies and financing through taxes Tiebout replied:  Spontaneous order could be provide by a locational market  Individuals make personal decisions about public goods in response to taxes (or prices) that they wish to pay  Although taxes paid to governments are compulsory, the ability to choose governments to whom to pay taxes makes payment of taxes voluntary 70

Hillman 2009: Chapter 3 Public goods Limitations of the Tiebout mechanism Employment opportunities: Is location for employment distinct from public-good choice? The scope of choice  Does the scope of choice replicate a competitive market for local public goods?  Public goods come in bundles: large numbers of alternative jurisdictions may be required to offer the sought-after combinations of quality and quantity. 71

Hillman 2009: Chapter 3 Public goods Norms and conventions as public goods  How to dress  How people entertain themselves, including being drunk in public places  Locational choice allows people to choose a community in which they feel comfortable 72

Hillman 2009: Chapter 3 Public goods The Tiebout mechanism when people seek different types of public goods The outcome is efficient supply of public goods within a jurisdiction 73

Hillman 2009: Chapter 3 Public goods Different quantities or qualities of the same public good The Tiebout locational mechanism is more complex when people want different quantities or qualities of the same public good Valuation and cost R V Loss of the high-benefit person from locating in S the low-benefit Tax per unit of the public good Z T J Loss of the low-benefit person from locating in the MB H F high-benefit jurisdiction MB L O Quantity G L G H Separation of low- and high-benefit people by choice of jurisdiction  Low-benefit person wants G L  The high-benefit person wants G H  Neither may be offered in this jurisdiction but people can move 74

Hillman 2009: Chapter 3 Public goods Locational choice among government jurisdictions solves the public-good preference revelation problem Natural monopoly and cost sharing We have not taken account of the attribute of natural monopoly of public goods The Lindahl voluntary-pricing consensus solution: Costs of supply per person are minimized by providing the public good in a single jurisdiction Efficient cost-sharing requires a single jurisdiction Separation into different jurisdictions for revealing information about preferences contradicts efficient cost sharing 75

Hillman 2009: Chapter 3 Public goods The second-best  The first-best Lindahl solution is not feasible  The Tiebout locational-choice solution is a second-best outcome when the first-best Lindahl solution is not available.  The second-best is the only feasible outcome: both revelation of preferences and cost minimization per person are not simultaneously possible 76

Hillman 2009: Chapter 3 Public goods Demonstrating the cost-sharing efficiency of a single jurisdiction In a jurisdiction, the government does not know personal Lindahl prices The government sets a common per-unit self-financing tax T P  . T n This is the minimum possible price or tax No Lindahl consensus: at the minimum tax or per unit price T , there is disagreement on the quantity or quality of the public good that low and high-benefit people want to have supplied 77

Hillman 2009: Chapter 3 Public goods Cost sharing in separate jurisdictions: We divide the population of n people   n n n . L H n L have MB L n H have MB H In separate jurisdictions, individuals’ personal per-unit payments are higher than in a combined jurisdiction: P P   T , T L H n n L H 78

Hillman 2009: Chapter 3 Public goods There are costs and benefits of separate jurisdictions  The cost of separation into in different jurisdiction is the need to pay the higher unit-taxes.  The benefit of separation is choice of public spending on public goods according to own preferences. There is a trade-off 79

Hillman 2009: Chapter 3 Public goods Valuation and cost R S MB H V Tax per unit of the public good D with two tax jurisdictions 2T E Y Tax per unit of the public good J Z with a single tax jurisdiction T H MB L F Quantity O G L1 G L G H1 G H The decision whether to form a separate jurisdiction n L =n H T : the per-unit tax in one jurisdiction 2T : the per-unit tax doubles in 2 jurisdictions Who controls the collective decision? The group in control of the choice of public-good supply has an incentive to attempt to block exit of others 80

Hillman 2009: Chapter 3 Public goods Tiebout and Lindahl   G G G L1 H 1 E The Lindahl consensus solution in a single jurisdiction is Pareto- improving compared to separate jurisdictions. Taxes and cost ∑ MB H ∑ MB L P = MC ∑ MB L + ∑ MB H MB L T H MB H T L Quantity or quality of the O G L1 G H1 G E public good Figure 3.17: The efficient Lindahl consensus and the outcome of separation People are trapped by incentives of asymmetric information in separate Tiebout jurisdictions 81

Hillman 2009: Chapter 3 Public goods Prices and politics in the Tiebout locational market  The Tiebout locational mechanism is a substitute for a market  Payments should be like the prices paid in any market  Price is a per-unit cost per person  In practice, taxes are levied on the value of property or housing, or on income, or a sales tax might be levied The Tiebout benefit principle of markets is compromised by politics  The benefit principle of payment required for the Tiebout mechanism can be politically unpopular, because the people who benefit are required to pay  The benefit principle does not allow cross-subsidization through political decisions 82

Hillman 2009: Chapter 3 Public goods A natural experiment  The government of Prime Minister Margaret Thatcher in the United Kingdom introduced the benefit principle to local public finance in 1988  In 1991 the property tax was restored  Widespread non-compliance with the tax per beneficiary of public services The benefit principle:  Introduced tax obligations for people who lived in public housing  and for people who lived in houses where there were more than average numbers of occupants  Taxes increased for occupants of less expensive houses. The policy experiment ended with successful popular (and political) resistance to the benefit principle for payment for local public goods. 83

Hillman 2009: Chapter 3 Public goods Income and locational rents  The Tiebout locational mechanism views people as differing only in preferences for public goods: income and wealth determine the public goods that people can afford  Zoning implements separation by income and wealth: housing in a jurisdiction may be expensive because zoning regulations permit only expensive houses  Exclusion through zoning regulations: high-income people exclude low-income people, who would live in low-valued housing and pay low property and income taxes but nonetheless would benefit from the jurisdiction’s public goods 84

Hillman 2009: Chapter 3 Public goods Housing prices include locational rents If not for the excess demand expressed in the locational rent, housing prices for identical houses would be the same in two jurisdictions Taxes would be higher in a richer area but the higher taxes would be precisely matched by the higher spending on local public goods A jurisdiction is “exclusive” when lower-income people, who would be prepared to pay higher taxes in order to receive higher-standard public goods, are excluded from a jurisdiction by locational rents that have increased housing prices. In all markets, demand depends on preferences, prices, and incomes or wealth 85

Hillman 2009: Chapter 3 Public goods Cost-sharing for public goods as a cooperation gam e There is no asymmetric information if personal benefits and costs are revealed  Wealth and possessions indicate benefits from public spending on law enforcement  The number of children is an indicator of benefits from public spending on schools  Owning a car is an indicator of benefit from a road People cannot seek to free ride by being deceptive when personal benefits and costs are known The problem is agreement on sharing of costs A cooperative game Apply the Nash bargaining solution 86

Hillman 2009: Chapter 3 Public goods Example: cars and trucks C 1 = payment by the car owner C 2 = payment by the truck owner C 1 = Cost of the car owner D 45 o 100 45 o A 40 2 1 20 B C 2 = Cost of the O 60 100 80 truck owner A bargaining outcome for cost sharing At point 2: separate roads, no agreement on cost sharing The cost of the road sufficient for the car owner = 40 The cost of the road required by the truck owner = 100 DB : efficient outcomes of one road and sharing of the cost 100 87

Hillman 2009: Chapter 3 Public goods Incentives  The owner of the car will share if C 1 < 40  The truck owner will share if C 1 > 0 Bargaining: Feasible bargaining outcomes (0 > C 1 > 40) are AB No agreement: separate roads at the disagreement (or threat) point 2 Pareto efficiency: outcomes along AB are superior to the point 2 Equal bargaining power: equal gains from cooperation are at point 1 The gains from cooperation: 20 each = 40 C 1 = 20 = (40 -20) C 2 = 80 = (100 -20) The outcome is the Nash bargaining solution for cooperative games 88

Hillman 2009: Chapter 3 Public goods 3 .3 COST– BENEFI T ANALYSI S Cost-benefit analysis is a last resort for obtaining information  The Clarke tax would, if used, provide information about personal benefits and costs  User prices provide information about MB of use: although costs of constructing a bridge are financed over time through toll charges, cost-benefit analysis is required when the bridge is built  The locational choice mechanism: cost-benefit analysis is required to evaluate the costs and benefits of public spending in a jurisdiction 89

Hillman 2009: Chapter 3 Public goods A. Costs and benefits w ithout m arket valuations Cost and valuation of the public good Max W = ∑ B – C MC=P ∑ MB O Quantity of the G E public good The objectives of cost-benefit analysis are (1) to determine if W = B – C > 0 (2) to determine efficient supply of a public good G E Examples: Markets do not exist that allow biodiversity to be valued A dam may disturb the habitat of a rare toad 90

Hillman 2009: Chapter 3 Public goods Often the objective is to determine whether W > 0 Sensitivity analysis is used to test how the estimates of cost and benefit affect calculations Examples:  Saving the rhino  The value of human life 91

Hillman 2009: Chapter 3 Public goods B. Valuation over tim e  The need to choose a discount rate  The case for a zero discount rate A high discount rate increases the likelihood that a project that harms the environment will pass the test of cost-benefit analysis 92

Hillman 2009: Chapter 3 Public goods A project with a one-time cost and a one-time benefit  B    1 W C 0.  0 (1 ) i If ∑ B 1 = 105 and C 0 = 100, the project is justified if i < 5% Choosing i > 5 percent ensures rejection of the project 93

Hillman 2009: Chapter 3 Public goods A project with benefits for multiple years       B C B C B C        1 1 2 2  N N W ( B C ) 0.    0 0 2 N (1 i ) (1 i ) (1 i ) When i > 0, we can define a discount factor 1    1.  1 i                    2 W B C B C B C 0 0 1 1 2 2 where  discounts the future. In the special case where benefits and costs are the same in each year and extend indefinitely into the future:    B C i i . W i 94

Hillman 2009: Chapter 3 Public goods What should the discount rate be?  Do returns in private capital markets reflect the time preference of people in society?  If the environment is a gift of nature that is not the possession of any generation, we should choose zero discounting  The distinction between social and private risk  Decisions made today affect yet unborn populations, who may not find acceptable the discount rate that was chosen in the past  We may wish that past generations had been more attentive to effects on the environment and had used zero or low discount rates 95

Hillman 2009: Chapter 3 Public goods C. The discount rate and choice betw een public projects The discount rate determines choice between alternative public investments Example: choice between public investment in a subway system and highway expansion 96

Hillman 2009: Chapter 3 Public goods Subw ay Highw ay Cost C 1,400 once 400 every 10 years Benefit each year B i 60 per year 50 per year A time horizon of 50 years Undiscounted total benefit ∑ B i 3,000 2,500 Undiscounted net benefit ∑ (B i -C) 1,600 500 Gain from choosing the subway 1,100 A time horizon of 100 years Undiscounted total benefit ∑ B i 6,000 5,000 Undiscounted net benefit ∑ (B i -C) 4,600 1,000 Gain from choosing the subway 3,600 Discounted at i = 5% Total benefit ∑ B i 1,200 405 every 10 years Total net benefit ∑ (B i -C) -200 +5 every 10 years 97

Hillman 2009: Chapter 3 Public goods D. I ncom e distribution and cost-benefit analysis Changes in incomes because of public spending  A bridge might provide greater benefits for high-income persons than for low-income persons because high-income persons have high value of time  Low-income people might have low incomes because they are cut off from high-income employment opportunities by the absence of a bridge: cost-benefit analysis should then take into account the future increase in the incomes of the low-income people 98

Hillman 2009: Chapter 3 Public goods Social justice The objective of the cost-benefit criterion is efficiency. When the cost-benefit criterion takes account of aspects of fairness or social justice, we need to weigh efficiency and social justice We shall use a social welfare function to introduce such weights when we study social justice. 99

Hillman 2009: Chapter 3 Public goods Cost-benefit analysis and political decisions  A political representative may succeed in obtaining public spending that benefits his or her constituency  If the public investment is not justified by cost-benefit analysis, the intended beneficiaries of the project are better off, if they are given the public money directly  Politicians may be unable to give away money, although they can provide publicly financed public-good projects 100