LECTURER: JACK WU

The Theory of Property Tax

Outline

Topic I: What Are Property Taxes?Topic II: Property Tax IncidenceTopic III: Property Tax CapitalizationTopic IV: Property Tax Competition and

Provision of Local Public Goods

Model of Property Tax Competition

Tiebout Model (1956)Tax-competition literatureA realistic model of property tax competition:

a blend of Tiebout and tax-competition traditions

Tiebout (1956)

Traditional thought: markets generally fail to provide public goods efficiently because of free rider problem. Therefore, the government intervention is required.

Tiebout (1956): the ability of individuals to move among jurisdictions produces a market-like solution to the local public goods problem.

Tiebout model (1956)

• Individuals vote with their feet and locate in the community that offers the bundle of public services and taxes they like best.

• Intergovernmental competition benefits consumers by generating a variety of public-good choices within a metropolitan area. This variety, which emerges as local governments compete to attract residents, leads to an equilibrium in which consumers efficiently self-select different communities according to their demand for local public goods.

• Each individual receives her desired level of public services and cannot be made better off by moving. Hence, the equilibrium is Pareto efficient, and the government action is not required to achieve efficiency.

Tiebout’s assumptions

• Government activities generate no externalities.• Individuals are completely mobile.• People have perfect information with respect to each

community’s public services and taxes.• There are enough different communities so that each

individual can find one with public services meeting her demands.

• The cost per unit of public services is constant.• Public services are financed by a proportional property

tax. The tax rate can vary across communities.

Tiebout Equilibrium Conditions

• Consumers choose their consumption bundles optimally.

• Consumers choose their regions of residence optimally (no households wishes to move, taking as given public good levels and taxes across regions)

• Firms maximize profits• Markets clear• Each regional government balances its budget• Each regional government’s public goods and tax

plan maximize its objective

Efficient Provision of Local Public Goods

Samuelson condition:

jg

jx

jg

j CUUN /

Tax Competition Literature

The literature has explored the bad side of intergovernmental competition, showing that each community sets its tax rate too low in an attempt to preserve its tax base.

Fiscal Interactions among governments

• Fiscal interactions may be the result of benefit spillovers, where residents of one jurisdiction consume the public goods provided by neighboring jurisdictions.

• Alternatively, interaction may arise because of interjurisdictional mobility of the tax base.

• The tax competition literature has focused on either interaction due to spillovers or interaction due to tax-base mobility.

Tax-competition models

Jurisdictions finance provision of a public good with a tax on locally-employed capital.

Capital is nationally fixed but moves among jurisdictions in response to tax-rate differentials, while community populations are typically immobile.

Two Versions of competitive models

• Version 1: jurisdictions are small relative to the economy and thus are unable to affect the net-of-tax return to capital. As a result, tax rates in other jurisdictions are irrelevant, and strategic behavior is absent.

• Version 2: when jurisdictions are large relative to the economy, each jurisdiction is able to alter capital’s net return by varying its tax rate. As a result, the tax rates in other jurisdictions must be taken into account in a given jurisdiction ‘s choice, leading to strategic behavior.

Important conclusion of tax competition model

Public goods are underprovided because each community keeps its tax rate low in an attempt to preserve its tax base.

A Realistic Model of Property Tax Competition

In such a model, consumers are mobile and self-select into homogeneous communities, which rely on property tax to finance public goods. Since concern about capital flight leads to low tax rates, the equilibrium has efficient sorting of consumers across communities, but it exhibits a tendency toward under-provision of public goods.

Basic Model

• Assumptions:• The metropolitan area consists of two

communities• The capital invested in community i (Ki) is

combined with a local fixed factor (Pi) to produce a numeraire private good according to a constant-returns technology.

• The local fixed factor can be viewed as labor supplied by local workers.

• The property tax is levied on the capital invested in community i with tax rate ti .

Production function

iiiiii PKkkfPKF /),(),(

Uniform net-of-tax return

2211 )()( tkftkf

Conditions

.2,1,0

.2,1,0

itk

it

i

i

i

Implication

Capital’s net return is reduced by higher taxes.

Higher taxes shrink community i’s tax base as capital relocates to equalize net returns.

Extended Model

• Assumptions:• The property tax is also levied on housing that is

produced using only land.• The quantity of residential land in community is fixed,

suggesting that housing supply is perfectly inelastic.• The tax rate on land = tax rate on capital=ti• Land’s net-of-tax return is ri and its gross price is ri+ti• The residents of the community owns equal share of

land.• The ownership of metropolitan area’s fixed capital

stock is divided equally among all consumers.

Land endowment and capital endowment per capita

21*

*

/

/

PPKk

PLq iii

Utility function

),,( iiii zqxU

Individual budget constraint

)()()(**

iiii

iiiiiii

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Government budget constraint

)( *iiii kqtz

Utility Maximization

)](,,)()([ ****iiiiiiiiiitkqtqqtkkfkkfUMax

i

First-order condition

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i

i

tk

iii

tiii

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iz

tqkkkqk

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** )(

Nash Equilibrium Condition

Assume consumers have identical preferences and community populations and residential land areas are equal. In this case, must hold in the Nash equilibrium, implying

*21 kkk

21 tt

First-Order Condition at Nash equilibrium

0,1**

**

i

i

tK

iix

iz

tk

tqkqk

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i

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Underprovided Public Goods

Since the marginal rate of transformation between private and public goods is unitary, this inequality implies that public good is underprovided.