Land and Property Taxes

Land and Property Taxes

Ram Singh

Lecture 2

Stamp Duty: Tax Evasion and Remedy I

Suppose

a buyer has already engaged in a property transaction at pricep^∗. A stamp duty tax needs to be paid on the “reported price"p.

t^Sdenote the stamp duty tax/rate the circle ratec.

π(.)is the probability of being investigated by the tax department and getting caught if and only if he under-reports

F is the fine

Stamp Duty: Tax Evasion and Remedy II

The buyer solves the following maximisation problem:

maxp {t^sp^∗−t^smax(p,c)−π(p)F} Assume:

π⁰(p)<0, π⁰⁰(p)>0, π(0) =1, π(p^∗) =0, F >0 (0.1)

−t^s−π⁰(c)F >0 (0.2)

The buyer compares the benefits of tax evasion against the costs. That is, t^s(p^∗−p)against the costsπ(p)F

The solution to to this maximisation satisfies the following FOC:

−t^s =π⁰(p)F (0.3)

Property Tax I

Property Tax

Annual tax on Annual Property Value (APV).

In Delhi the unit area method is used to calculate the annual property value

is calculated by multiplying unit area value assigned to the colony/locality by the covered area of the property

depends on factors such as age, structure of the property and nature of use.

Let

Lbe the land area

Property value beV =pK^αL^1−α, whereK is the amount of capital investment.

Property Tax II

p=1. So, value of property isV =K^αL^1−α t^pbe the property tax

r be the cost of capital

r be the same for all types of properties

In the absence of property tax, the OP of the landowner : maxK K^αL^1−α−rK

The profit maximizing investment solves : K^∗ = (α

r)

1 1−αL

Property Tax III

In the presence of property tax, the OP of the landowner : max

K (1−t^p)K^αL^1−α−rK The profit maximizing investment solves :

K^∗∗= (α(1−t^p)

r )

1 1−α

L

Clearly, under tax the optimal level of value improving activityK^∗∗ is less than K^∗.

Property Taxes: Tax Revenue

Let

T =t^pV denote the tax revenue collected from a property That is,

T =t^p((α(1−t^p)

r )

1 1−α

L)^αL^1−α Hence,

T =t^p(α(1−t^p)

r )

α 1−α

L T is increasing function of tax rate,t^p, only when:

(1−t^p)^1−αα −t^p α

1−α(1−t^p)^{2α−11−α} >0 That is,

1−t^p> α Or,

t^p<1−α

Property Tax based on Location I

Let

adenote the index of locational amenities where the property is located Nowthe value of a house is now:

V =p(a)K^αL^1−α wherep⁰(a)>0

In the absence of tax, the OP for the landowner is: The FOC yields:

K^∗= (αp(a) r )

1 1−α

L

Let

t^pbe tax rate (per-unit) of property value

Property Tax based on Location II

Now, the OP of the landowner becomes:

maxK {(1−t^p)p(a)K^αL^1−α−rK} The FOC yields:

K^∗∗= (αp(a)(1−t^p)

r )

1 1−α

L

An increase in the tax ratet^pleads to a decrease in the equilibrium level of investment

An increase in the index of locational amenitiesaand hencep(a)leads to an increase in the equilibrium level of investment.

Clearly, for givena,

K^∗∗<K^∗

Property Tax based on Location III

Note that for givena, K^∗−K^∗∗ = (^αp(a)_r )

1

1−αL[1−(1−t^p)^1−α1 ]

K^∗∗

K^∗ = (1−t^p)^1−α1 The tax collected is given by

T^P(t^p,a,L) =t^pp(a)(K^∗∗)^αL^1−α

Locally Funded Public Good

Assume

there is only one property owner provision forais funded by property tax g(a)be the cost ofa

Consider the following social welfare

maxt^p,a{(1−t^p)p(a)K^αL^1−α−rK +t^pp(a)K^αL^1−α−g(a)}

s.t.t^pp(a)K^αL^1−α=g(a).

Question:

Find out optimal mix ofaandt^p IsK =K^∗∗= (^αp(a)(1−t_r ^p))

1 1−αL? IsK ><K^∗?

Land Tax I

The maximisation problem of the landowner now looks like : maxK p(a)K^αL^1−α−rK−(t^L)L The FOC for optimization yields :

K^L=p(a)(α

r)^1−α1 L=K^∗

Clearly, the optimal level of value improving activityK^Lequals its efficient levelK^∗.

The tax revenue is given by

T^L(t^L,a,L) =t^LL

Land Tax II

Consider

two localities- 1 and 2 with different locational advantages,a₁anda₂; a₁>a₂. Sop(a₁)>p(a₂),

two parcels of same size - one in each locality t^Las land tax

Surplus accruing to landowners in the two regions are:

π₁=p(a1)(K^αL^1−α)−rK−t₁^LL

π₂=p(a2)(K^αL^1−α)−rK−t₂^LL

Land Tax III

The optimization exercise of the landowners in the two regions yields:

K₁^∗= (αp(a1) r )^1−α1 L

K₂^∗= (αp(a₂) r )^1−α1 L It can be seen thatπ₁(K₁^∗)> π₂(K₂^∗). Consider

π₁(K₁^∗) =p(a₁)(K₁^∗αL^1−α)−cK₁^∗−t₁^LL=0 π₂(K₂^∗) =p(a₂)(K₁^∗αL^1−α)−cK₂^∗−t₂^LL=0 That is, the tax rates are given by:

t₁^L>t₂^L (0.4)