By John F. Sase
For Julie, whose patience, encouragement, and support helped me see this to completion.
I. INTRODUCTION
There has been an increase in agglomerative sub-centering over the past two decades in many large metropolitan areas. What present society describes as urban sprawl or suburban flight may simply be a natural process of urban-regional development, consistent with monocentric urban thought and development extending backwards in time for more than two millennia. By objective, this theoretical work emulates major monocentric models developed over the past three millennia to develop an extended mathematical model with agglomerative subcenters.
Next, our empirical work tests this extended model against observations of Major Retail Centers (MRCs) for radially monocentric SMSAs. Through a two-step econometric technique which includes a model-specification error test, the results ascertain the existence and locations of peak subcenter activity at an average of approximately one-half the distance between from the Central Business District and the furthest MRC.
This position concurs with Plato's ideal model of Magnesia and other works of the past three millennia. Fundamentally, the inspiration and intuition for this article comes from a lifetime of oral and written cultural tradition. Building upon this tradition, this work uses the historical chronicles and analyses found in chapter two to develop the theoretical model in chapter three. In retrospect, the empirical results in chapter four support the theory of peak subcenter activity developed in chapter three.
II. THE HISTORICAL WORK
We may divide the literature forming the background for this writing into three major areas: historical origin, theoretical development, and empirical testing. The second chapter traces the historical origins of the monocentric urban models which justify the development of agglomerative employment subcenters. Our history asserts that monocentric urban-regional models may have roots that are more ancient than previously reported.
Though Professor Paul Samuelson and others trace the monocentric model back to the Isolated State of Johann Heinrich von Thünen, evidence of monocentric urban models and monocentric sites exists which dates from before the time of Plato. This chapter traces the monocentric urban concept in western thought and by so doing provides material with which to extend the Standard Urban Model. In addition, this chapter also uncovers ancient variations to the concentric-ring model including radial pathways and employment subcenters.
The literature on the historical origins comes from inter-disciplinary sources and lends support to an extensive tradition of monocentric urban thought. More specifically, this literature extends backwards in time by more than two millennia. It lends historical support to the theory of agglomerative subcenters used in the present theoretical model and empirical testing. The literature employed to develop the primitive origins of Monocentric Cities primarily come from the fields of anthropology, archaeology, and philosophy. The treatment of Middle Eastern roots draws in works from the fields of religious and cultural studies. The section on the culmination of monocentric urban thought in ancient Greece includes the writings of Plato and commentaries on Plato by modern writers.
This literature relevant to thought during the early Christian era includes scriptural sources, early religious writing, and modern commentaries on these writings. The modern development of the model includes earlier models found in the Utopian Literature of the Age of Enlightenment and later models which stem from the utopian tradition, enveloping modern economic thought.
Current models that follow earlier traditions appear in standard present-day works.
Economic Literature forms the basis for the extended model developed within the theory chapter of this series. The purpose of the historical research has chronicled the evolution of monocentric thought and provides material with which to generate an extended standard urban model in Part Three.
In response to the development of major urban subcenters in recent decades, the need exists for revised models, consistent with the existent standard model, that sufficiently address recent urban growth issues. The general evolution of monocentric thought uncovers a number of ancient variations. These variants remain useful in the development of revised models and a few of these help in the development of revised models in the third part of our tale.
III. THE THEORETICAL WORK
Three areas of monocentric literature lend themselves to the development of the theoretical model in chapter 3. These areas include monocentric models in general, urban employment subcenters, and agglomeration economy as applicable to subcenters.
In respect to monocentric models in general, the ancient works of Plato, John of Patmos, Saint Augustine, and various medieval works that include those of Saints Thomas More and Campanella, provide roots for the modern works of Von Thunen, Howard, Park and Burgess, Losch, Alonso, and Mills. These provide the basis for the development of the extended agglomerative model. Furthermore, the more current works of McDonald and Bowman and others add further support to the use of the negative-exponential function along with related measures for determining urban gradients.
Authors Moses and Williamson, White, Tauchen and Witte, MaCauley, and Yinger directly address the issue of suburbanization of employment, business subcenters, and agglomeration economies. Moses, and Williamson, more specifically address the issue of subcenters in respect to the minimization of transportation costs. White presents evidence for the existence of employment subcenters. Tauchen and Witte further discuss the issue of agglomeration economies as applied to business centers and subcenters. MaCauley updates the work of Mills specifically including suburbanization of retailing relevant to this work.
Yinger applies his analysis of business centers to three-dimensional space that includes the use of the double integral function (which is used, similarly, in the current model developed in this article.
Part III of this work develops an urban model with Employment Centers and Subcenters that result from bidding among competing users and from agglomeration economies. Generally, urban models consider rent as measured only in respect to the radial dimension expanded from the urban center.
However, within this model, competitive bidding between businesses and residential users for urban land leads to an analysis of rent with respect to both the radial and lateral dimensions in a monocentric city expressed in a polar coordinate space. This urban model emulates Plato's allegorical city of Magnesia and other ideal models reviewed within this writing. The city contains a small number of equidistant radial highways that extend from from the Central Business District (CBD). A large but finite number of streets laterally cross the highways.
Commuters and transporters choose the radial highway system that minimizes travel costs to off-highway locations. As a result, they generally limit travel to one of the uniform radial segments. Therefore, we can analyze the process of “sub-centering,” as generalized from one radial segment. In the first part of this writing, we have developed a simple model of land allocation through competitive bidding. Initially, bidding among users results in a business area concentrated around the CBD, tapering outward along the radial highway.
Our analysis departs from the standard urban model by way of the introduction of compound lateral bid-rent functions for both business and residential users. The combination of a negatively sloped normal business bid-rent function and a very steep negatively sloped premium-bid function for highway frontage produces a negatively sloped upper-envelope lateral bid-rent curve. However, subtracting a negatively exponential disamenity residential bid-rent function from a normal negative-exponential function produces a lateral-residential, bid-rent curve. This curve, which initially has a positive slope, reaches a maximum a short distance from the highway, and then becomes negatively sloped thereafter. This action results in land apportionment to the dominant bidder at each location point. Bidding apportions all land located near the CBD (Central Business District). However, increasing the percentage of land going to residential bidders at distances further from the CBD, results in a bidding apportionment that produces a business center that tapers outward along the radial highways.
In the second part of this missive, we will develop a subcenter-case of land allocation through competitive bidding.
The bid-rent profile changes through the introduction of an avoidance-rent phase toward the radial dimension of the residential bid-rent surface. We will see that the avoidance-rent segment maintains a positive slope at intermediate distances. As a result, changes in competitive bidding results in a reallocation of land. Such reallocation produces a business subcenter close to the urban limit.
————————
Adapted from my Doctoral Dissertation (Wayne State University, 1992)
————————
Dr. John F. Sase teaches Economics at Wayne State University and has practiced Forensic and Investigative Economics for twenty years. He earned a combined M.A. in Economics and an MBA at the University of Detroit, followed by a Ph.D. in Economics from Wayne State University. He is a graduate of the University of Detroit Jesuit High School (www.saseassociates.com).
For Julie, whose patience, encouragement, and support helped me see this to completion.
I. INTRODUCTION
There has been an increase in agglomerative sub-centering over the past two decades in many large metropolitan areas. What present society describes as urban sprawl or suburban flight may simply be a natural process of urban-regional development, consistent with monocentric urban thought and development extending backwards in time for more than two millennia. By objective, this theoretical work emulates major monocentric models developed over the past three millennia to develop an extended mathematical model with agglomerative subcenters.
Next, our empirical work tests this extended model against observations of Major Retail Centers (MRCs) for radially monocentric SMSAs. Through a two-step econometric technique which includes a model-specification error test, the results ascertain the existence and locations of peak subcenter activity at an average of approximately one-half the distance between from the Central Business District and the furthest MRC.
This position concurs with Plato's ideal model of Magnesia and other works of the past three millennia. Fundamentally, the inspiration and intuition for this article comes from a lifetime of oral and written cultural tradition. Building upon this tradition, this work uses the historical chronicles and analyses found in chapter two to develop the theoretical model in chapter three. In retrospect, the empirical results in chapter four support the theory of peak subcenter activity developed in chapter three.
II. THE HISTORICAL WORK
We may divide the literature forming the background for this writing into three major areas: historical origin, theoretical development, and empirical testing. The second chapter traces the historical origins of the monocentric urban models which justify the development of agglomerative employment subcenters. Our history asserts that monocentric urban-regional models may have roots that are more ancient than previously reported.
Though Professor Paul Samuelson and others trace the monocentric model back to the Isolated State of Johann Heinrich von Thünen, evidence of monocentric urban models and monocentric sites exists which dates from before the time of Plato. This chapter traces the monocentric urban concept in western thought and by so doing provides material with which to extend the Standard Urban Model. In addition, this chapter also uncovers ancient variations to the concentric-ring model including radial pathways and employment subcenters.
The literature on the historical origins comes from inter-disciplinary sources and lends support to an extensive tradition of monocentric urban thought. More specifically, this literature extends backwards in time by more than two millennia. It lends historical support to the theory of agglomerative subcenters used in the present theoretical model and empirical testing. The literature employed to develop the primitive origins of Monocentric Cities primarily come from the fields of anthropology, archaeology, and philosophy. The treatment of Middle Eastern roots draws in works from the fields of religious and cultural studies. The section on the culmination of monocentric urban thought in ancient Greece includes the writings of Plato and commentaries on Plato by modern writers.
This literature relevant to thought during the early Christian era includes scriptural sources, early religious writing, and modern commentaries on these writings. The modern development of the model includes earlier models found in the Utopian Literature of the Age of Enlightenment and later models which stem from the utopian tradition, enveloping modern economic thought.
Current models that follow earlier traditions appear in standard present-day works.
Economic Literature forms the basis for the extended model developed within the theory chapter of this series. The purpose of the historical research has chronicled the evolution of monocentric thought and provides material with which to generate an extended standard urban model in Part Three.
In response to the development of major urban subcenters in recent decades, the need exists for revised models, consistent with the existent standard model, that sufficiently address recent urban growth issues. The general evolution of monocentric thought uncovers a number of ancient variations. These variants remain useful in the development of revised models and a few of these help in the development of revised models in the third part of our tale.
III. THE THEORETICAL WORK
Three areas of monocentric literature lend themselves to the development of the theoretical model in chapter 3. These areas include monocentric models in general, urban employment subcenters, and agglomeration economy as applicable to subcenters.
In respect to monocentric models in general, the ancient works of Plato, John of Patmos, Saint Augustine, and various medieval works that include those of Saints Thomas More and Campanella, provide roots for the modern works of Von Thunen, Howard, Park and Burgess, Losch, Alonso, and Mills. These provide the basis for the development of the extended agglomerative model. Furthermore, the more current works of McDonald and Bowman and others add further support to the use of the negative-exponential function along with related measures for determining urban gradients.
Authors Moses and Williamson, White, Tauchen and Witte, MaCauley, and Yinger directly address the issue of suburbanization of employment, business subcenters, and agglomeration economies. Moses, and Williamson, more specifically address the issue of subcenters in respect to the minimization of transportation costs. White presents evidence for the existence of employment subcenters. Tauchen and Witte further discuss the issue of agglomeration economies as applied to business centers and subcenters. MaCauley updates the work of Mills specifically including suburbanization of retailing relevant to this work.
Yinger applies his analysis of business centers to three-dimensional space that includes the use of the double integral function (which is used, similarly, in the current model developed in this article.
Part III of this work develops an urban model with Employment Centers and Subcenters that result from bidding among competing users and from agglomeration economies. Generally, urban models consider rent as measured only in respect to the radial dimension expanded from the urban center.
However, within this model, competitive bidding between businesses and residential users for urban land leads to an analysis of rent with respect to both the radial and lateral dimensions in a monocentric city expressed in a polar coordinate space. This urban model emulates Plato's allegorical city of Magnesia and other ideal models reviewed within this writing. The city contains a small number of equidistant radial highways that extend from from the Central Business District (CBD). A large but finite number of streets laterally cross the highways.
Commuters and transporters choose the radial highway system that minimizes travel costs to off-highway locations. As a result, they generally limit travel to one of the uniform radial segments. Therefore, we can analyze the process of “sub-centering,” as generalized from one radial segment. In the first part of this writing, we have developed a simple model of land allocation through competitive bidding. Initially, bidding among users results in a business area concentrated around the CBD, tapering outward along the radial highway.
Our analysis departs from the standard urban model by way of the introduction of compound lateral bid-rent functions for both business and residential users. The combination of a negatively sloped normal business bid-rent function and a very steep negatively sloped premium-bid function for highway frontage produces a negatively sloped upper-envelope lateral bid-rent curve. However, subtracting a negatively exponential disamenity residential bid-rent function from a normal negative-exponential function produces a lateral-residential, bid-rent curve. This curve, which initially has a positive slope, reaches a maximum a short distance from the highway, and then becomes negatively sloped thereafter. This action results in land apportionment to the dominant bidder at each location point. Bidding apportions all land located near the CBD (Central Business District). However, increasing the percentage of land going to residential bidders at distances further from the CBD, results in a bidding apportionment that produces a business center that tapers outward along the radial highways.
In the second part of this missive, we will develop a subcenter-case of land allocation through competitive bidding.
The bid-rent profile changes through the introduction of an avoidance-rent phase toward the radial dimension of the residential bid-rent surface. We will see that the avoidance-rent segment maintains a positive slope at intermediate distances. As a result, changes in competitive bidding results in a reallocation of land. Such reallocation produces a business subcenter close to the urban limit.
————————
Adapted from my Doctoral Dissertation (Wayne State University, 1992)
————————
Dr. John F. Sase teaches Economics at Wayne State University and has practiced Forensic and Investigative Economics for twenty years. He earned a combined M.A. in Economics and an MBA at the University of Detroit, followed by a Ph.D. in Economics from Wayne State University. He is a graduate of the University of Detroit Jesuit High School (www.saseassociates.com).
