1. Incentivizing Development to Maximize Property Value
Tu Nguyen
Advisor: Dr. Marc Ordower
Presented to the Department of Mathematics
in partial fulfillment of the requirements
for a Bachelor of Science degree with Honors
Randolph College
Lynchburg, Virginia
May 6, 2015
2. 1
Abstract
Greenfield development is considered the solution to address two problems in the United States:
increasing housing demand because of the growing population and expanding local government
budget deficits as a result of the recent global financial crisis. Greenfield development can tackle
these problems through effective zoning practices. This paper develops time-dependent
dynamical models to test how using incentives might help build high-quality and livable
communities while maximizing property value. The results show that there is an inverse
relationship between the number of parklands and the total property value. As a result, there is a
trade-off between having more parklands and maximizing property value.
3. 2
Table of Contents
Chapter 1: The Two Problems …………………………………………………………………... 3
Chapter 2: Greenfield Development …………………………………………………………….. 4
Chapter 3: Traditional Zoning vs Performance Zoning …………………………………………. 6
Chapter 4: Models ……………………………………………………………………………….. 8
Chapter 5: Results ……………………………………………………………………………… 17
Chapter 6: Discussion ………………………………………………………………………….. 38
References ……………………………………………………………………………………… 41
4. 3
Chapter 1
The Two Problems
It was estimated that the United States population would grow by almost 58 million people
during the period 2003-2025, which is about one sixth of the current population. Because of the
limited availability of natural resources, particularly land, a problem arises: How can we find
housing for this new population? Many people see infills, the redevelopment and revitalization of
obsolete and underutilized buildings, as a method to meet the increasing demand for housing.
However, Heid (2004) was afraid that infill strategies cannot happen fast enough to make any
difference by 2025 [1]. In addition, infill redevelopment is often costly because it involves
several steps ranging from purchasing land, removing existing buildings, and cleaning up
environmental contamination onsite [2] [3]. As a result, infill redevelopment is not the ideal
solution to satisfy the new demand for housing.
In addition, it is found that since 2010, there have been 47 municipal bankruptcy filings. Many
local governments across the U.S. still face steep budget deficits [4]. The question is, how can
these financially struggling municipalities find a way to get out of the deficit?
These two completely different problems, fortunately, have a similar solution. These two issues
can be addressed at the same time by practicing greenfield development.
5. 4
Chapter 2
Greenfield development
Greenfield development refers to the process of creating planned communities on previously
undeveloped land in the vicinity of a city. The land used is usually farmland. Following is a list
of characteristics of a greenfield:
Be rural or really low-density land.
Contain significant natural, cultural, or agricultural resources.
Be located outside recognized urban limits.
In addition, Heid (2004) also noted that greenfield development is capable of building high
quality, diverse living environments and is also the most practical and affordable method to build
without sprawl [1]. Furthermore, it has been proven to cost less than infill development [2].
As shown, greenfield development is a viable solution to the problem of finding housing for the
new population. In addition, it also helps tackle the second problem of local government budget
deficits by increasing property value.
Campbell (1951) found that property taxes are the main mechanism through which local
governments raise revenues. The basic formula to determine property taxes is
𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑡𝑎𝑥 = 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 × 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒.
Consequently, to increase the amount of property taxes, a local government can either raise the
current tax rate or try to increase the market value of all the properties in the area. The first
method of raising the current tax rate is not feasible since it often faces opposition from local
6. 5
residents. On the other hand, the second method can be achieved through effective zoning
practices.
7. 6
Chapter 3
Traditional Zoning vs Performance Zoning
Zoning is an urban planning tool used by local governments to better relocate their resources and
to segregate uses that are incompatible to protect the property value. Land uses are often divided
into three main categories: residential, commercial, and industrial. In addition, there are several
zoning approaches: Traditional or Euclidean zoning, performance zoning, incentive zoning, and
form-based zoning. The two common types that will be discussed in this paper are Euclidean
zoning and performance zoning.
Euclidean zoning segregates different categories of land uses into separated zones to avoid
incompatible uses. For example, if an area is zoned residential, no commercial buildings are
allowed to be built in the area. Although it is a common approach in the United States, the
traditional zoning method has faced criticism for several decades for its inflexibility. Reps (1964)
pointed out that the separation of land uses can prevent mixtures of uses even though it is more
desirable [5]. For example, it might be more beneficial to have a grocery store in a residential
area rather than locating all the grocery stores in just one place. As a result, alternatives to the
traditional zoning practice have been developed to address its problems.
An alternative to the traditional zoning method that is commonly used in many countries is
performance zoning. Performance zoning establishes a set of goal-oriented and performance
standards to regulate land development. Some examples of the performance standards are setting
a limit on the noise level in a neighborhood and protecting the natural environment. The
8. 7
performance zoning method provides the flexibility and transparency not inherent in the
traditional method. In addition, it also tends to create more diverse and livable communities.
In this paper, the performance zoning approach was used to create a model of greenfield
development in a small city with the criteria of maximizing property value and enhancing
livability. The next section will cover the models used.
9. 8
Chapter 4
Models
Time-dependent dynamical models are developed in Excel on a grid of size 6x8, with each cell
representing one farm. Different from typical zoning practices, in this paper, four categories of
land uses are included: single-family residential, multi-family residential, commercial, and
parkland. Industrial use is left out because the city considered in this study is relatively small and
thus is not heavily industrialized. In addition, parkland is included to create a livable
neighborhood. It should be noted that each farm may be purchased and developed by a separate
developer. Additionally, each developer is going to make development decisions to maximize his
profit. The city government cannot require how the development should take place.
6
5
4
3
2
1
_ _ + _ _ _ _ _
1 2 3 4 5 6 7 8
Figure 1. A 6x8 grid of greenfield land.
In the model, these four uses were abbreviated as below:
P – Parkland.
S – Single-family residential.
M – Multi-family residential.
C – Commercial.
10. 9
In addition, the underscore signs “_” represent the highway and the plus sign “+” signify an
enter/exit to and from the highway. Number 0 is used to indicated an undeveloped cell. As a
result, Figure 2 shows how the grid looks like at time 0.
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
_ _ + _ _ _ _ _
Figure 2. Initial configuration
It is important to note each of these cells may be developed into a 2x2 grid of city blocks and
each block in the 2x2 grid maybe developed to a purpose, independently of how the other blocks
are developed. For example, a cell named “SPCM” represented four street blocks with their
respective order as follows:
S P
C M
Figure 3. Street blocks contained in a cell.
From now on, I will refer to each of those small blocks as “blocks” and the cells containing 4
blocks as “cells”. From the definition of a cell as described above, there are 44
= 256 possible
combinations of blocks in a cell. In other words, every cell can be in one of the 256 possible
states.
11. 10
A developer would only have the incentive to purchase an undeveloped lot if it generates the
highest potential positive profits. The value of a cell to the developer is determined from the
following formula:
𝑉𝑎𝑙𝑢𝑒 𝑡𝑜 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑟 = 𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 − 𝑈𝑛𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 − 𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡.
Where,
The undeveloped value is the cost of purchasing a piece of farmland.
The development cost takes into account all the four costs of developing each street block in a
cell. Generally speaking, building a multi-family residential property from a greenfield land costs
the most while developing parkland is the cheapest.
The development value is the potential value of a cell. It consists of the value determined from
how far away a cell is from the highway and of internal and external values, both of which are
again potential values. Generally speaking, the closer to the highway, the higher value a cell has.
The internal value of a cell is the total value from each of the four blocks in a cell, which is based
on the existence of other blocks in the cell. Each of the 256 possible cells has its own internal
value. For example, let’s consider the cell “SMCC”. The internal value of this cell is calculated
by adding the value of each individual block: S, M, C, and C. The value of C, for example, is
based on the number of S and the number of M in the cell itself.
The external value of a cell, on the other hand, depends on the states of all the cells that are of
one distance away from it. For example, the external value of cell (2,3) is derived from the states
of the following four cells: (2,2), (2,4), (1,3), and (3,3). Let’s consider the following example.
12. 11
MPMS
MCCC SPMC CCCC
PCCS
Figure 4. The external value of a cell.
The middle cell, “SPPC”, has an external value that is derived from the other four surrounding
cells. Its external value is calculated by adding the value to each block in the cell, namely S, P,
M, and C, from the surrounding cells. Note that the potential external value of a cell is influenced
by surrounding blocks that were already developed.
From these definitions, it can be seen that at time 0, each of the 48 cells may have a positive
potential internal value from some combinations of blocks but only has a zero potential external
value since no cells have been developed yet.
Following is the list of benefit functions:
For internal value:
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑃 = 0.
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑆 =
12
(#𝑃)2
− 1 × (#𝑆)2
+ 6 × (#𝑆) + 4.5 × (#𝐶).
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑀 =
12
(#𝑃)2
+ 8 × (#𝐶).
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝐶 = 4 × (#𝑆)2
+ 8 × (#𝑀).
For external value:
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑃 = 0.
13. 12
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑆 =
8
(#𝑃)2
− 0.5 × (#𝑆)2
+ 5 × (#𝑆) + 3 × (#𝐶).
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑀 =
8
(#𝑃)2
+ 2.5 × (#𝐶)2
.
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝐶 = 2 × (#𝑆)2
+ 8 × (#𝑀).
Note that in the above cases, when #𝑃 = 0, the benefit from parkland was set to be equal to 0.
In both cases, 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑃 was assumed to be 0 because parkland would bring no profit to the
developer.
For the internal values, 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑆 was a function of the number of surrounding parklands,
single-family residential properties, and commercial properties. It was believed that
𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑆 would have the highest value if there was one nearby parkland. The higher the
number of parklands, the lower the benefit. In addition, having a dense neighborhood would be
beneficial, but only up to a point. After that, there would be a problem of overcrowding. As a
result, a downward-opening parabola was chosen to measure the influence of surrounding single-
family residential properties. Finally, not surprisingly, the higher the number of nearby
commercial properties, the higher the value to S. A household would love to be able to go
shopping and get groceries within walking distances.
Using the same reasoning, 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝑀 was a function of the number of parklands closeby and
the number of surrounding commercial properties.
14. 13
Additionally, 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑡𝑜 𝐶 depended on the number of single-family and multi-family
residential properties nearby. Every commercial company would appreciate having a large
customer base in the surrounding area as it can make more profits. Hence, the higher the number
of surrounding single-family and multi-family residential properties, the higher the benefit to C.
Finally, the same logic was applied to compute the external values for P, S, M, and C. However,
the benefits derived from surrounding neighborhoods would have a lower multiplier, taking into
account the distance away.
Regarding the costs to a developer, the undeveloped value was fixed at 70 and the development
costs for P, S, M, and C were 2, 5, 10, and 9 respectively.
Finally, the process of running the development is outlined as below:
1. List all the combinations of blocks for each cell.
2. Calculate the potential internal values and the potential external values for each
combination.
3. Weigh in the development cost and the undeveloped value to compute the value to the
developer for each combination.
4. Compare all the values to the developer and determine the maximum positive value.
Choose a combination that has the highest value for the cell being considered.
5. Do steps 1-4 for all the cells in the model.
6. After all the cells have been considered, move on to the next time period. Note that once
a cell has been developed, it will not change throughout the rest of the model.
15. 14
Several models were conducted in this study. For the first model, a developer would develop his
lot rationally, that is by trying to maximize his profit. For the later models, an incentive was
introduced into those models and again development was also conducted rationally. It is believed
that the decisions of developers working independently based on their own profit do not
necessarily coincide with those of the municipal government nor the current and future residents
of this region. As a result, the local government will try to incentivize development through
grants to maximize livability and property value, with access to parkland being used as a
measure of livability. The incentive considered was a grant from the local government to the
developer for developing a parkland within a cell. With this grant, for models 2-4, the
undeveloped value was now lower for all the cell states containing parklands and remained 70
for all other combinations. In addition, a different type of incentive was introduced to model 5,
which helped pay for the cost of building a parkland. In other words, the development cost for P
was 0 in model 5.
From the above description of the models used in this study, it is relatively straightforward to
realize that these models are actually a slight variation of a cellular automaton. A cellular
automaton is a discrete, abstract computational system of simple, homogenous objects, called
“cells”. These cells have the following characteristics:
1. The cells live on a grid.
2. Each cell has a state. The number of state is generally finite. For the simplest case, there are
two possible states, 0 or 1. In addition, at each discrete time step, each cell is in only one
state.
16. 15
3. Each cell has a neighborhood. This is typically a set of directly adjacent cells.
These cells evolve through a number of discrete time steps according to a set of propagation
rules. These rules specify how a cell will develop based on the current state of its neighboring
cells.
As seen, to model a system using cellular automata, one will have to define the dimension of the
grid, specify the number of states a cell can have, and construct a function that governs the
evolution of each cell based on its neighboring cells’ current state. The cells will then evolve in
discrete time steps according to the set of propagation rules. The definition of a cellular
automaton is relatively straightforward. However, generally the propagation rules must be
chosen carefully to allow researchers to have meaningful and interesting results.
Cellular automata have been used to model and study natural systems. For example, these
biological and physical systems have been modelled effectively using cellular automata: Urban
development, gas behavior, the flow of electricity in a power grid, and life itself.
In this paper, the time-dependent dynamical models do resemble a cellular automaton. The field
in this study is a two-dimensional grid of size 6 by 8. In addition, each cell can have one of 256
possible states. Finally, the propagation rules in this system are a function that maximizes the
value to a developer from a single cell. However, there are some modifications from a typical
cellular automaton. First, instead of having to set an initial configuration for the system at time 1
in a typical cellular automaton, the propagation rules in this study will govern the initial
17. 16
configuration at time 1. Second, different from a normal cellular automaton, each cell in this
model, after being developed, will not change its state in the next time steps. This means after a
cell is developed as “SPCC” at time t, its state will remain “SPCC” at time t+1, t+2, t+3, etc.
Finally, generally most cellular automata do not have a concrete orientation, in the sense that it is
hard to tell the position of a cell in the grid. However, in this project, The Cartesian coordinate
system is used to specify each point in the grid. This modification is needed to tracks the value
that comes from the distance from a cell to the highway.
39. 38
Chapter 6
Discussion
As can be seen from the previous section, there are no parklands in the first model while there
are several parklands in the second model. This helps achieve the goal of having high quality and
healthy living environments. This finding shows that a developer is still capable of building a
livable community while maximizing his own interest.
In addition, if the grant amount to encourage having a parkland is reduced to 10 from the original
amount of 15, the number of parklands decreases while the total property value rises. On the
other hand, if the grant amount is increased to 22, the number of parklands increases while the
total property values falls. With the parameters used in the model, 22 is the maximum grant
amount that can be given because if the grant amount goes over 22, the whole first row will be
developed at time 1, which is not realistic. Recall from the first chapter that besides developing a
livable community, the other goal of the paper is to conduct zoning effectively so that the
property value, and thus government revenues, is maximized. Unfortunately, these two goals
cannot be achieved at the same time. There is a trade-off between having more parklands and
maximizing property value. Figure 5 and Figure 6 demonstrates the inverse relationship between
these two variables.
40. 39
Figure 5. Total property value as a function of the grant amount.
Figure 6. Number of parklands as a function of the grant amount.
26300
26400
26500
26600
26700
26800
26900
27000
27100
27200
27300
0 5 10 15 20 25
Totalpropertyvalue
Grant amount
Total Property Value
0
2
4
6
8
10
12
0 5 10 15 20 25
Numberofparklands
Grant amount
Number Of Parklands
41. 40
This study has several limitations. First, the greenfield area considered in this study is relatively
small. It might be better to include a larger area. Second, most of the parameters chosen are
arbitrary. Future researchers should consider using actual data to see the impacts of performance
zoning in real life. Finally, in the study, I only consider the influence on a cell’s external value
from cells that are one-distance away. A more generalized model that takes into account the
influence from farther away cells would be worth investigating.
42. 41
References
[1] Heid, J. (2004). Greenfield development without sprawl: The role of planned
communities. Washington, DC: Urban Land Institute.
[2] Porter, M (1995). "The Competitive Advantage of the Inner City". Harvard Business Review:
55–72.
[3] Farris, J. T. (2001). "The barriers to using urban infill development to achieve smart growth".
Housing Policy Debate 12 (1): 1–30.
[4] Governing. (2014). “Bankrupt Cities, Municipalities List and Map”. Retrieved from
http://www.governing.com/gov-data/municipal-cities-counties-bankruptcies-and-defaults.html.
[5] Reps, J. W. (1964). Requiem for zoning. Department of City and Regional Planning, Cornell
University.
