The Theory of Property Tax
LECTURER: JACK WU
Outline
 Topic I: What Are Property Taxes?
 Topic II: Property Tax Incidence
 Topic III: Property Tax Capitalization
 Topic IV: Property Tax Competition and Provision of
Local Public Goods
Topic II: Property Tax Incidence
 II1:Traditional View: Excise Tax View
 II2:New View: Capital Tax View
Traditional View
 Property tax is viewed as an excise tax貨物稅.
 Therefore, property tax is ad valorem tax從價稅.
 Theoretical analysis approach: Partial equilibrium
analysis
New View
 Property tax is viewed as a capital tax 資本稅or
profit tax利潤稅.
 Therefore, property tax is a factor tax要素稅.
 Theoretical analysis approach: General equilibrium
analysis
II1: Traditional View: Property Tax as Excise Tax
 Case 1:Tax on Land
 Case 2:Tax on Structure (Building attached to land)
Case 1:Tax on Land
 Natures of Land:
_Fixed quantity
_Immobility
_Durable
 Assumptions on Land: Supply of land is perfectly
inelastic
Figure: Incidence of a Tax on Land
Summarizing Incidence of a Tax on Land
 Neutral
 Efficient (no deadweight loss)
 Tax Burden borne completely by landlords

Case 2:Tax on Structure
 Natures of Structure:
_Heterogeneity
_Immobility
_Durability
_High moving cost
_Discrimination and Segregation
 Assumptions: Supply of structure is perfectly elastic
Figure: Incidence of a tax on structure
Summarizing Incidence of a Tax on Structure
 Neutral
 Tax burden borne completely by structure users
 Inefficient (Deadweight loss)
Progressive or Regressive?
 Progressive: property tax as a percentage of income
rises with income
 Regressive: property tax as a percentage of income
falls with income

Figure: Estimates of the Property Tax as a Percentage of Income
under the Traditional View , 1957 (Netzer)
Unit: $1,000; %
Money
Nonresident Residential
income class ial property property
Total
property
Less than 2
4.0
3.3
7.3
2-3
3.4
1.6
5.0
3-4
3.2
1.4
4.6
4-5
3.4
1.4
4.8
5-7
2.2
1.7
3.9
7-10
1.6
2.0
3.6
10-15
1.3
2.7
4.0
15 and over
1.7
1.6
3.3
Average
-
-
4.6
Regressive
14
 Netzer , D. 1966. The Economics of Property Tax. Brookings Institute. Table 3.3, p.45 and Table 3.5, p.55.

Figure: Estimates of the Property Tax as a Percentage of Income
under the Traditional View , 1968 (Musgrave)
Unit: $1,000; %
Income class
Total property
Less than 4
6.7
4.0-5.7
5.7
5.7-7.9
4.7
7.9-10.4
4.3
10.4-12.5
4.0
12.5-17.5
3.7
17.5-22.6
3.3
22.6-35.5
3.0
35.5-92.0
2.9
92.0 and over
3.3
Average
3.9
15
Regressi
ve
 Musgrave R.A. and Musgrave P.B 1973. Public Finance in Theory and Practice. McGraw-Hill. p. 368.

Figure: Estimates of the Property Tax as a Percentage of Income
under the Traditional View , 1966 (Pechman and Okner) Unit: $1,000; %
Family income
class
Total property
Less than 3
6.5
3-5
4.8
5-10
3.6
10-15
3.2
15-20
3.2
20-25
3.1
25-30
3.1
30-50
3.0
50-100
2.8
100-500
2.4
500-1,000
1.7
1,000 and over
0.8
Average
16
3.4
Regressi
ve
 Pechman, J.A. and Okner B.A. 1974. Who Bears the Tax Burden? Brookings Institute. Table 4.8, 3b, p. 59.

Figure: Estimates of the Property Tax as a Percentage of Income
under the Traditional View , 1970 (ACIR)
Unit: $1,000; %
Family income
class
Residential
property
Less than 2
16.6
2-3
9.7
3-4
7.7
4-5
6.4
5-6
5.5
6-7
4.7
7-10
4.2
10-15
3.7
15-25
3.3
25 and over
2.9
Average
4.9
Regressi
ve
 Advisory Commission on Intergovernental Relations.17
1973. Financing Schools and Property Tax Relief–A
State Responsibility. ACIR. Table 15, P. 36.
II2:New View: Property Tax as Capital Tax
 Rationales of Capital Taxes
 Incidence of Capital Taxes
-Case 1:A Uniform Tax
-Case 2:Differential Taxation by Types
-Case 3:Differential Taxation by Locations
 Impacts of Property Tax Differential on Labor
market, local consumer goods market, and land
market
Rationales of Capital Taxes I
 Modern economic analysis most often
considers property taxes as taxes levied on
the capital, which is one of the major inputs
(with labor and materials) into the
production of goods and services.
 It is straightforward that property taxes are
levied on commercial and industrial
property because plant, land, and equipment
are considered as capital.

Rationales of Capital Taxes II
 Residential housing is not intuitively considered as
capital. Alternatively, they are normally considered
as durable consumer good.
 However, physical residential housing can be
considered as only one input into the production of a
consumer good: housing service.
Incidence of Capital Tax
 Case 1: A Uniform Tax
 Case 2: Differential Taxation by Types
 Case 3: Differential Taxation by Locations
Case 1: A Uniform Tax
 Assumption 1: The quantity supplied of capital goods
(property) in the nation is fixed (in the long run),
suggesting a perfectly inelastic supply of capital.
 Assumption 2: The government imposes a uniform
national tax on all capital goods (property) at a single
rate. This implies that changes in the type of property
owned or the location of the property will not reduce the
tax liability. The only way to avoid the tax is to reduce the
amount of property owned, that is, to reduce investment.
 Assumption 3: A property owner cannot avoid the tax by
selling the property to another investor.
Implications
 After the tax is imposed and known, any potential
buyer would be willing to offer less for the property
because the future after-tax return is lower than it
would be if there were no tax. Therefore, the
property tax is represented by a shift down in the
demand curve.
Figure. Incidence of Uniform Tax
Summary of Incidence of A Uniform Tax
 Tax burden borne entirely by capital owner. The rate
of return earned by capital owners falls by the full
amount of the tax because those owners at the time
the tax is levied have no options to change behaviors
in an effort to avoid the tax.
 Efficient (NO distortion, NO deadweight loss)
Case 2: Differential Taxation by Types
 Assumption 1: Two types of capital goods: A and B
 Assumption 2: Government levies a property tax on
capital A, while it levies zero tax on capital B
 Assumption 3: Investors can avoid the tax by
decreasing their investment in taxable capital and
increasing their investment in exempt capital.
 Assumption 4: Capital goods are mobile between
types.
 Assumption 5: Users of capital goods are immobile
between capital types.
Implication of Assumption
 Reality: some types of property are exempt from
taxation with all other property taxed everywhere at
a uniform rate.
 Distortion in capital investment decision: Investing
more on capital B (exempt capital) and less on
capital A (taxable capital)
 As a result, after-tax rates of capital return change:
after-tax rate of return of capital A rises and after-tax
rate of return of capital B falls.
 In equilibrium, after-tax rate of return of capital A
equals after-tax rate of return of capital B

Figure: Very Short Run
28
Very Short Run Analysis
 Initial equilibrium is at rate of return R0 for two
types of capital (A and B) when there are no taxes.
 If a property tax is imposed on Capital A only, the
immediate effect is a reduction in the rate of return
from capital A to R1, as reflected by DA1, which
includes the tax. An investor in capital A earns a
return of R0, pays tax of (R0-R1), and retains a
return of R1. Because the tax has reduced the rate of
return from capital A compared to that available
from capital B, investors are expected to switch from
A to B in the short run.

Figure: Short Run Adjustment
30
Short Run Analysis
 As the amount (quantity supplied) of capital A falls
from A0 to A1, the rate of return from capital A
changes to R2, and as the supply of capital B rises,
the price of , or the rate of return from, capital B
falls to R2.
 Potential investors in capital B need not be offered
as high a return when there was no tax on A,
because the property tax on capital A has made
investment in capital B relatively more attractive.

Figure: Long Run Equilibrium
32
Long Run Analysis
 The long-run equilibrium is reached at quantities A1
and B1, with a net-of-tax rate of return in both
markets equal to R2.
 Of course, owners of capital A still have to pay the
tax; so to earn a net-of-tax rate of return equal to R2,
they must receive a gross return of R3.
Long-Run Equilibrium
 In capital A market:
Price paid by capital user: R3
Price received by capital owner: R2
Capital tax per unit: R3-R2
Both capital user and owner share tax partially
 In capital B market:
Price paid by capital user= Price received by capital owner: R2
Capital user gains, but capital owner loses.
Incidence of Differential Taxation by Types
 Tax burden is borne by capital owners of both types
 Tax burden is borne by capital users of Type A
 The capital user of Type B benefits from tax
 Inefficient
Why does differential taxation create inefficiency?
 The tax differential creates an incentive for the economy
to have more of the untaxed capital, even though the
productivity of capital B has not risen.
 The initial long-run supply represents the marginal social
cost for both types of capital and initial demand the
marginal social benefit.
 The tax differential induces an increase in the amount of
capital B so that marginal cost is greater than marginal
benefit. Similarly, the reduction in the amount of capital
A causes its marginal benefit to be greater than marginal
cost. In other words, the economy is supplying too much
capital B and too little capital A.

Figure: Dead Weight Loss
37
Case 3: Differential Taxation by Locations
 Assumption 1: All capitals are homogeneous
 Assumption 2: Two locations: A and B
 Assumption 3: Government levies a property tax on
capitals in location A, while it levies zero tax on
capitals in location B.
 Assumption 4: Capitals are mobile between locations
 Assumption 5: Capital users are immobile between
locations
Implications of Assumption
 Reality: taxation of identical property at different tax
rates by different jurisdictions.
 Capital owners can avoid the property tax in location
A by moving to location B.
 In equilibrium, the after-tax rates of return in both
locations are equal.

Figure: Very Short Run
40
Very Short Run Analysis
 Initial equilibrium is at rate of return R0 for two
locations (A and B) when there are no taxes.
 If a property tax is imposed on Capital in location A
only, the immediate effect is a reduction in the rate of
return from capital in location A to R1, as reflected by
DA1, which includes the tax. A capital investor in
location A earns a return of R0, pays tax of (R0-R1),
and retains a return of R1. Because the tax has reduced
the rate of return from capital in location A compared
to that available from capital in location B, investors
are expected to switch from location A to location B in
the short run.

Figure: Short Run Adjustment
42
Short Run Analysis
 As the amount (quantity supplied) of capital in
location A falls from A0 to A1, the rate of return
from capital in location A changes to R2, and as the
supply of capital in location B rises, the price of , or
the rate of return from, capital in location B falls to
R2.
 Potential investors in capital in location B need not
be offered as high a return when there was no tax
on capital in location A, because the property tax
on capital in location A has made investment in
capital in location B relatively more attractive.
Figure. Long Run Equilibrium
Long Run Equilibrium
 The long-run equilibrium is reached at quantities A1
and B1, with a net-of-tax rate of return in both
locations equal to R2.
 Of course, owners of capital in location A still have to
pay the tax; so to earn a net-of-tax rate of return
equal to R2, they must receive a gross return of R3.
Incidence of Differential Taxation by Locations
 Tax burden borne by capital owners in both locations.
Some of the tax burden from the higher-tax location
is shifted to capital owners in the lower-tax location
through the decrease in the rate of return, which is
caused by the increased supply.
 Tax burden borne by capital users in Location A
where capitals are taxed.
 Capital users in Location B where capitals are not
taxed benefit from the tax.
 Inefficient
Figure. Deadweight Loss
Modified Case 3: Assumption 5 is dropped
 What happen if we drop the assumption 5 that
capital users are immobile?
 Users of capital in location A pay a higher rental
price than that in location B, so some of them will
move to location B.
 Therefore, the demand for capital in location A
decreases, and the demand for capital in location B
increases.

Figure: Long Run Equilibrium with Mobile Capital Users
49
Long-Run Equilibrium with mobile capital users
 There is no long run equilibrium under this setting
because it is impossible that both equilibrium
conditions hold simultaneously: (1)equalized rental
prices paid by capital users in both locations, and (2)
equalized rental prices received by capital owners in
both locations.
 The long run equilibrium outcome depends on the
relative spatial mobility of capital owners and users.
Impacts of Differential Taxation by Locations
 Impacts on labor market
 Impacts on local consumer goods (Housing services)
 Impacts on land market
Analysis of Impacts on Labor Market
 If capital is mobile, the higher tax rate in location A
causes less capital to be invested in that location,
which is expected to affect the demand for labor in
location as well.
 If labor and capital are complementary, then the
reduced amount of capital investment will also
reduce the demand for labor, causing wages in
location A to fall.
 The opposite happens in location B, where
increased capital investment causes an increase in
demand for labor and an increase in wages.
Figure. The impact on Labor Market, Labor is
Immobile
Labor is immobile
 If workers do not or cannot change jobs in response
to these wage changes, the story stops; part of the
differential property tax burden in location A has
shifted to workers in location A.
Labor is Mobile
 However, if workers are mobile and respond to the
change in relative wages, the supply of labor falls in
location A (driving wage back), and the supply in
location B rises (driving wage down). In that case,
the effect of the property tax differential in location A
is a reduction in employment rather than a change in
wages.
Figure. The impact on Labor Market, Labor is Mobile
Impacts on Local Consumer Goods
•
•
•
The changes in the user prices of capital in locations A and B,
caused by the difference in property taxes, also are expected to
affect the prices of local consumer goods that use capital in their
production process.
Because the user's price of capital (the rental rate) has increased
in location A, one expects that the prices of local consumer
goods that are capital intensive will also rise.
Housing service is the chief among these local consumer goods.
Figure. The impact on local consumer goods,
consumer is immobile
Analysis (Immobile consumer)
 In location A, the supply curve shifts up because
the cost of producing housing services increases
due to the higher property tax. As a result, the
price of housing services in location A -that is, the
consumer’s cost of living in a house- is expected to
rise. It rises from P0 to P1.
 In contrast, the decrease in the consumer’s price of
capital in location B is expected to reduce the price
of housing services in location B. (Supply curve of
housing services shifts to the right).
Figure. The impact on local consumer goods,
consumer is mobile
Analysis I(Mobile Consumer)
•
•
Just as with labor, whether the story stops or continues depends
on whether housing consumers respond to the change in the
relative price of housing services between the two locations.
If consumers are aware of the differences and are mobile, then
more consumers are expected to seek housing in B, where the
price has decreased, and fewer consumers are expected to seek
housing in A.
Analysis II(Mobile Consumer)
 However, the decrease in housing demand in
location A will housing prices down, while the
increase in housing demand in location B will
increase housing prices again.
 If consumers are perfectly mobile, the resulting
effect of the property tax differential, then, is a
decrease in the amount of housing in A and an
increase in the amount of housing in B, but the
relative prices do not change.
Impacts on Land Market
•
•
•
Because of the positive property tax rate
differential in location A, the amount of capital
investment in A is expected to fall, with the effect
of decreasing the demand for the complementary
input land.
Further, if housing consumers react to the
increased housing service price by leaving for
other locations, the demand for land will decline
further.
These decreases in the demand for land will
reduce the price (value) of land in A.
Impacts on Land Market II
•
•
However, landowners do not have the option,
available to owners of other types of capital, of
moving their investment (land) to a lower-tax
location; the supply of land in location A is fixed.
If all other capital, other inputs, and consumers
are all mobile, then the burden of the tax
differential that remains is reflected in a decreased
value of land.
Impacts on Land Market III
If land is the only immobile commodity or agent,
then all of the burden of the tax differential is
capitalized into land values in the higher-tax
location, A in the example.
 Those hurt by the tax differential are the
landowners in location A at the time the tax was
increased. Landowners in location B benefit.
•
Figure. The impact on land market
Summary
Property Tax Rate  in location A
 Wage ; Employment 
Price of local goods ; Production
output 
Housing rent ; Land rent 
Value of houses and land 