Lecture on Household Sorting, Local Government and Public Goods

Lecture on Household Sorting, Local Government and Public Goods Based on Chapter 13 and 19 in Urban Economics by Arthur O’Sullivan, 5th edition and Chapter 14 of The Economics of Zoning Laws by William Fischel Adapted and summarized by Austin Troy, University of Vermont

What is the role of government? • Stabilization: monetary and fiscal policy used to control unemployment and inflation • Redistribution: Taxation and transfers used to remedy inequities • Resource allocation: makes production decisions either directly (e.g. through municipal utility) or indirectly (e.g. through subsidies or taxes on allocations). • See Musgrave and Musgrave (1980)

Local Government • Does not have the responsibility of fiscal stabilization for obvious reasons • Does not have redistributive role because of mobility of citizens. Poor will immigrate and rich will emigrate to other city • Both of these roles are better filled by national government • Local government primarily fills third role

When does local government intervene in resource allocation? • Provides goods produced under natural monopoly conditions • Provides goods that generate positive externalities • Provides public goods

Externalities • Represent a “market failure” • Where one person or firm’s consumption of a good creates benefits or costs for others • Individual makes a personally efficient decision (I.e. consumes until MB=MC) but externality causes there to be a social cost or benefit that is not considered; socially inefficient • Causes divergence between private and social benefits and/or costs • The cost or benefit is not “internalized” by producer

Positive Externalities (e.g.education) Marginal social benefit E’=how much market would provide E*=socially optimal amount Marginal private benefit Marginal cost Subsidy amt E’ E*

Negative Externalities (e.g. pollution) P’=pollution produced in private market P*=optimal pollution amount K=amount of externality Marginal social benefit Marginal social cost K Marginal private cost Marginal private benefit P* P’

Natural Monopoly • Where production of a good subject to large scale economics: that is, very big fixed costs, so those costs don’t get paid off until the scale of operation gets very large • Private firms would underprovide service because high scale economies mean that average cost> marginal cost • City must step in and make up deficit

Natural Monopoly in Bus Service Demand= MB P’ LRAC deficit P* LRMC S’ S*= optimum Quantity

Natural monopoly • Problem is that firm producing at optimal point (S*) will lose money because D curve shows people not willing to pay that much • But there is a social cost to not having enough bus service, so to get residents to buy the socially optimal amount, P must be lower than market price; locality must make up this difference

Public Goods Provision • Local governments provide goods that the market cannot provide either because they cannot price it, charge for it, or exclude

Public Good Characteristics • Nonrivalrous: can be consumed by many at once, such as clean air • Pure local public is were MC of additional user=0; does not decrease other’s utility • Semi-rivalrous: where is non-rivalrous at small amounts or at certain times but not at others • E.g. streets may be non-rivalrous at certain times of day but not others

Public Good Characteristics • Nonexcludable: impossible/impractical to exclude any from consuming • Examples: Defense, air waves, other examples? • Hard to charge for the service • Can’t tell who is willing to pay and who is not, who is benefiting and who not • Some are non-excludable by choice, because alternative would be inequitable • Examples fire service

Pure and Partial Public Goods • A common situation is that goods are non-rival at smaller usage levels, but rivalrous at large usage levels • Example: with a park, an additional household’s use does not diminish anyone’s enjoyment, until you reach carrying capacity C at which point each marginal user does impose additional costs

Pure Public Goods $ per capita AC MR=AR Community size

Congestion point: here additional people start imposing cost on others This is the optimal size, because it minimizes average cost of services (AC) Partial Public Goods MC Additional user are welcome until congestion costs (MC)>AC, at N1 $ per capita AC MR=AR N0 N1 N2 Community size

Local Public Goods • These are public goods where the benefit is confined to a contained geographic area, like a city. • Ideally, the size of jurisdictions would be determined by the level of “localness” of the public goods being provided • The more extensive the benefits, the larger the jurisdiction need to internalize those

Why provide certain public goods at the local level? • Wallace Oates (1972) proposed three criteria: • Diversity of Demand: “one size fits all” vs. local diversity of preferences • Externalities/spillovers: are external effects locally contained or do they spill over? • Scale economies: higher levels of government can leverage bigger scale economies • The test for local provision of a public good is whether 1 outweighs 2 and 3

Tradeoff 1: Scale Economies v. Diversity of Demand • Assume 1 public good (library service) and two municipalities in metro area • High Demand in city H and low in L • No externalities/spillovers between towns • Scale economies: regional library can produce unit “literary services” cheaper than local library • Identical services in towns

Who should make library allocation? • If towns merge and form metro government, pool resources to build bigger library system, then good news is that cost/ unit service is lower, but bad news is that L is paying for more library service than they want and H is getting less library services/person than it had before. • Only efficient to merge if savings due to scale economies are large relative to losses in efficiency from the uniformity of service provision

Empirical Results • Moderate scale economies in things like sewer and water provision, because capital intensive • Police, fire and schools, have scale economies (gains to scale) occurring until about 100,000 people, at which point fewer gains to consolidation • Some areas have regional government entities that provide services with large scale economies

Tradeoff 2: Externalities vs. Demand Diversity • Where service creates positive externalities that spill over into other jurisdictions, it will be underprovided, because they consider the costs but, not all the benefits • Inefficiency occurs because boundaries of jurisdiction is too small to contain benefits

Example: Water pollution • Town X in the Champlain Valley will underprovide stormwater management services (unless mandated) because benefits are realized by all Lake Champlain users, and they only consider local benefits

Example: Parks Provision • Cities will tend to underprovide parks, because only consider benefits to local residents, when their parks could potentially be important resource for people regionally • However, if a regional government takes over and DD is high, there will be too many parks for certain types of people and too few for others

Diversity of Demand and Spillovers If externalities small, S’ will be close to S*, M’ close to M*, etc. This is efficient, unless DD is very large and S* is far from M* etc. Town M: medium parks Town L: large parks Town S: small parks MSB(l) MSB(s) MSB(m) MLB(l) MLB(s) MLB(m) S’ S* M’ M* L’ L*

Tradeoffs in level of PG provision: summary • If DD is large relative to scale economies or spillovers, local is better • If spillovers or scale economies are large relative to DD, then regional is better • In previous slide, gaps between individual demanders are greater than gaps between MSB and MLB, so local provider is better

Examples • Which category do these services fall into and why? • Flood control • Structural fire protection • Wildfire protection • Air quality • University system • Highway patrol

How much of a public good should a city provide? • Park example: how big to make it? • Assumptions: decisions made by majority rule, three-person city, no congestion, no spillover benefits • Efficient amount: where MB of additional acre equals MC • To get MB we add up everyone’s demand curves, which represent WTP

How big should park be? Cost/acre Marginal social benefit= MB1+MB2+MB3 MC $60 MB curves for three citizens MB1 MB2 MB3 70 acres Here WTP > MC of additional acre Here WTP < MC of additional acre

Methods for determining the amount of local public good • Benefits taxation: ideal, but impractical • Median voter: practical and common, but inefficient • Household mobility and sorting: practical and efficient under some conditions, but not necessarily equitable

Benefit taxation • This will yield optimum amount of local public good park (say, the park), even if population is heterogeneous • Tax people on their WTP for park ; the greater the WTP, the greater the tax • Impractical because must know shape of everyone’s demand curves and because there is no incentive for taxpayers with high WTP to reveal that willingness

Median Voter Approach • Assuming there is no interjurisdictional mobility • Often such decisions made through vote • Will efficient size be chosen? • No, not when charged by benefits taxation • This is because the Q will be chosen where the median voter’s private MB= marginal private cost, or tax • MC= $60/acre so each citizen pays $20/acre

Park provision under voting Cost/acre Marginal social benefit= MB1+MB2+MB3 Marginal social cost $60 MB1 Marginal private cost MB2 $20 MB3 10 55 70 acres 115

Median voter rule • In election between 115 and 55 acres, 55 would win because person 3 and person 2 would vote for it. In election between 10 and 55, 55 would win because person 1 and person 2 would vote for it. • Where spending level vs. service is being voted on the median voter’s desired outcome gets the most votes. • Inefficient because everyone pays equally, but some want it more than others • The magnitude of persons 1 and 2’s preferences don’t matter because median will always win

Urban differentiation and mobility • Now let’s assume there is inter-urban mobility • Households sort among different municipalities • Cities compete for residents • Market defined by the service bundle provided and the “entry price” • Service bundle made up of assortment of “public goods.”

Voting with feet: Interjurisdictional mobility • Charles Tiebout model (1956) explains how differences in pricing and provision of services define jurisdictions, and residents “shop” for those bundles. • Tiebout model suggests that interjurisdictional mobility might prevent median voter inefficiencies

Tiebout model assumptions • Households choose municipality providing ideal level of public goods • There is perfect information and costless mobility • There are no interjurisdictional spillovers • No scale economies: assume linear cost curve—not dependent on output • City pays for public goods with head tax

Tiebout and the park example • Mobility will increase intra-city homogeneity • Park lovers all go to one city with big parks, and those who value other uses for their money over parks sort themselves in a different city • Park size will be efficient within each city • In this case, the median voter is irrelevant

Tiebout model and sorting • Each household moves to the jurisdiction that maximizes utility by providing the best bundle of public goods relative to taxes • At a low quantity of public good, benefits>costs for all households, but as increase amount, costs>benefits for lower income households • Hence low income households outbid high income people in low public good areas and vice versa.

Tiebout model and sorting Bid rent: high income HH Bid rent: low income HH Where tax outweigh benefits of public goods for rich Low inc zone high inc zone Where tax outweigh benefits of public goods for poor

Tiebout model and sorting • Because public goods are income elastic, high income households will have larger MB from consuming public goods than low income, therefore steeper BR functions and will outbid where level of PG is high • Hence when HH’s sort themselves based on public goods will sort based on income—this is because income determines MB

Congestion point: here additional people start imposing cost on others According to Tiebout, this is the optimal size, because it minimizes average cost of services (AC) Tiebout model from government perspective MC Additional user are welcome until congestion costs (MC)>AC, at N1 $ per capita AC MR=AR N0 N1 N2 Community size

Tiebout model from government perspective • Because most local public goods are not pure (I.e. are semi-rivalrous), local governments will try to get communities that minimize AC of services rendered, by nudging them as close to N1as possible. • Hence, communities that are smaller will encourage development and communities that are bigger, or nearing that size will use growth controls.

Fischel Amendment to the Tiebout model • In some cases, though, N1(min point for AC), is not efficient point to be at • If town does not have monopoly zoning power (does not affect prices in metro area), efficient level is now N2, where MC intersects MR/AR • Means last household to move in is WTP exactly amount that costs community in additional provision services

A B C D N1’ Tiebout model from government perspective MC $ per capita AC A MR=AR If N1’, town is too small because costs BD imposed on community, but perceived benefit by prospective residents in AD. As long as new residents pay at least BD, town is no worse off N2 N0 N1 N2= Optimal size without monopoly zoning power Community size

N1 or N2? • Where all residents share costs equally, they all pay average costs and population would optimally not exceed N1; reason is that at N1, new residents pay same as old residents (AC), while they impose larger marginal costs (BD) than earlier residents. The rest of the community loses difference between MC and AC ( BC). This community will phase out new development

What if no controls? MC $ per capita AC A MR=AR That’s bad for the community, because MC> MR after N2; from there until N3 it benefits newcomers, but at the expense of previous residents New residents will arrive until size= N3 N2 N0 N1 N3 Community size

Tiebout model: empirical evidence • Greater the number of municipalities to choose from in metro area, the more homogeneous each is (Gramlich and Rubinfeld 1982) • Municipalities are more numerous and smaller in metro areas with more variation among citizens in terms of demand, based on things like income, age, etc (Fisher and Wassmer 1998)

Tiebout model and property tax • Hamilton (1975) made Tiebout model more realistic by changing entry price from head tax to property tax • Head tax: all pay equal amount; property tax: those with expensive houses pay more • Assume 50% houses big (300k) and 50% small ($100k) • City must raise average of $3k/ HH • To do this they have 1.5% rate, resulting in $4.5k in tax for big HH and $1.5k for small

How does Property Tax Affect Location Choice? • Big households now pay $4,500 but only get $3,000 in services • They could set up own municipality with only expensive houses so that they can lower the tax rate and all households pay for the level of services they get • They will do this if gains to doing so are large relative to transaction costs • They will enforce this in new town through use of large lot zoning, keeps property values high • This leaves small house town with big tax burden

Lecture on Household Sorting, Local Government and Public Goods