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?
1. Provides goods produced under natural
monopoly conditions
2. Provides goods that generate positive
externalities
3. 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
Marginal
private
benefit
Marginal cost
E’
E*
E’=how much
market would
provide
E*=socially
optimal
amount
Negative Externalities (e.g.
pollution)
P’=pollution
produced in
private market
Marginal social benefit
Marginal social cost
K
Marginal private cost
Marginal
private
benefit
P*
P’
P*=optimal
pollution amount
K=amount of
externality
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
Quantity
S’
S*= optimum
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 nonrival 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
Partial Public Goods
MC
Additional user
are welcome until
congestion costs
(MC)>AC, at N1
$ per
capita
AC
MR=AR
Congestion
point: here
additional
people start
imposing cost
on others
This is the optimal size,
because it minimizes average
cost of services (AC)
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:
1. Diversity of Demand: “one size fits all” vs. local
diversity of preferences
2. Externalities/spillovers: are external effects locally
contained or do they spill over?
3. 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
small,
Spillovers IfS’externalities
will be close to S*,
Town S:
small parks
MLB(s)
S’ S*
Town M:
medium parks
MSB(s)
MLB(m)
M’ M*
Town L:
large parks
M’ close to M*, etc.
This is efficient, unless
DD is very large and
S* is far from M* etc.
MSB(m) MLB(l)
L’ L*
MSB(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
Cost/
acre
How big should park be?
Marginal social benefit=
MB1+MB2+MB3
MC
$60
MB curves
for three
citizens
MB1
MB2
MB3
Here WTP > MC of
additional acre
70 acres
Here WTP < MC of
additional acre
Methods for determining the
amount of local public good
1. Benefits taxation: ideal, but impractical
2. Median voter: practical and common, but
inefficient
3. 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
Cost/
acre
Park provision under voting
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
Low inc zone
high inc zone
Where tax outweigh
benefits of public
goods for rich
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
Tiebout model from government
perspective
MC
Additional user
are welcome until
congestion costs
(MC)>AC, at N1
$ per
capita
AC
MR=AR
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)
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
Tiebout model from government
perspective
MC
$ per
capita
AC
A
A
MR=AR
B
C
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
D
N0
N1 N1’ N2
Community size
N2= Optimal size without
monopoly zoning power
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
N0
New residents will arrive
until size= N3
N1
N2
Community size
N3
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
Effects of Property Tax
• Increases the number of jurisdictions because leads
to more sorting
• Now sorting based not just on desired level of
public goods, but on housing consumption
• Under head tax only sort based on local public good
preferences
• I.E. There would be high public good/small lot
town, high public good/large lot town, etc.
• When households sort based on housing
consumption, they also sort based on income
because housing is a “normal good”
Racial Sorting
• Facts: 2/3 blacks live in central cities and 1/3
in suburbs; reversed for whites.
• Dissimilarity index: to achieve same racial
composition within a neighborhood as within
metro area, what percentage of the people
would have to move?
• The average for the US is 69%
• The larger the metro area, the more
segregation there is
Causes of Racial Sorting
• Empirical studies find blacks prefer to live in
more integrated neighborhoods than whites
on average
• Income sorting generally leads to racial
sorting because of correlation
– Nevertheless, a black HH with same
income/characteristics as white suburban HH is
still less likely to live in suburbs, disparity must
be explained by something else (Rosenthal 1989,
Kain 1985). What??
Real Estate Practices and Racial
Sorting
• Racial Steering: Real estate agents “steers” minority
homebuyers towards certain neighborhoods(Ondrich
1998)
• Often minority housing is of lower quality relative to
price compared to housing in white neighborhoods
(Milgram 1988, Krivo 1995)
• Minorities often given poorer levels of service in
information and financing (Yinger 1998)
• “Fair housing audits” now increasingly common
Neighborhood Transition
• Galster (1990) found that change in racial
composition is key factor in transitions in
Cleveland
• Factors determining change are initial black pop
share, white segregation attitudes and proximity
of neighborhood to minority-dominant
neighborhoods
• Three curves: a) average preferences , b) strong
segregation preferences and c) affirmative
marketing scenario
Changes in Racial Composition
1979-1980
Will be 30% black
in 1980
C=
affirmative
marketing
B=strong
segregation prefs
10%
A= average
prefs
Black majority by 1980 for A if
initial is greater than 37%
Percent Black in 1970 20%
37%
Changes in Racial Comp
• A neighborhood becomes more black, but stays fairly
integrated
• B neighborhood experiences high degree of “white
flight” so becomes more black, due to preferences of
whites, unless initial share of blacks is low
• Affirmative marketing increased black share
considerably in largely white neighborhoods
• Achieves racially balanced neighborhoods where not
adjacent to all black neighborhood; where adjacent to
black-majority neighborhood, did not work