從都市發展區塊規模探討冪次係數變化：複雜科學與經濟觀點之探索

Power Law Coefficient Variation in Growth of Urban Development Lumps: An Exploration based on Complexity Science and Economic Perspectives

柯博晟(PO-CHEN KO)

指導教授 ： 賴世剛

國立臺北大學/公共事務學院/都市計劃研究所/碩士(2009年)

摘要

所謂的都市發展理論，係指為了增加對都市發展是如何發生、都市是如何運作的理解與詮釋，而針對都市發展的現象、過程進行聚焦且逐漸累積而形成的研究與典範(paradigm)；「都市經濟學」和「複雜理論」即是當前都市發展議題研究的兩個主要途徑，然而以複雜理論為基礎的新興典範在1980年代以後已逐漸發展，並產生與傳統都市經濟學為基礎的典範有所不同之思维(如突現論、整體論、與非線性的動態世界觀)和分析方法，本研究即立基於兩典範已經發展的成果上，探討典範之間的關係，及其如何再造都市的空間系統與對都市的複雜現象之解釋。

再者，學術界在過去的研究中，都市的冪次現象(power law)皆一再地於都市發展過程中被觀察到，如Zipf(1949)、Rosen 與Resnick(1980)等的實證研究，而所謂的都市冪次現象，探討的是都市發展的規模結構與人口空間分佈所具有的某種特性，對此傳統都市經濟典範以經濟理論為基礎來探討這樣都市規模聚集與形成的原理，如Christaller(1933)，而複雜科學典範則以複雜理論的角度詮釋之，如Chen與Zhou(2003)；本研究便依據Anas等人(1998)所建議的方式：以傳統都市經濟的聚集經濟模式和複雜理論的非經濟模式(如遞增報酬)做結合，建立一種簡單的九宮格二維平面空間模式，嘗試作為結合經濟理論的觀點與複雜系統思维的可能的方式。

本研究九宮格模式以Arthur(1990a；2000)的遞增報酬機制與非線性路徑相依的隨機過程概念為基礎來進行實驗，依循本文所提出模式規則的運算結果顯示出：(1)空間中不同規模大小的都市聚落其形成的機率期望值與其規模間會反映出符合實證數據之冪次係數值，且小聚落發生頻率高，大聚落則較低；(2)在以遞增報酬機制為基礎的狀態下，所獲得的冪次係數值相較於無遞增報酬假設的狀態下，要更趨近於真實都市體系(等級大小法則所提出的-1斜率值)；(3)在本文中比較討論了九宮格模式、非線性波利亞過程之實驗(Chen,2004)、與基於遞增報酬為基礎的電腦模擬(于如陵，2005)等三種模式，結果顯示以于如陵的隨機成長模式在表現空間的相鄰關係與聚集效應層面上較為佳(數值較接近實證研究值)。

關鍵字

都市發展理論 ； 都市經濟學 ； 複雜理論 ； 冪次係數值 ； 遞增報酬 ； 九宮格模式

並列摘要

The theories of urban development help to enhance our understanding and explanations of how urban development has taken place and worked. They are formed into the research and paradigms by focusing on the phenomena and processes of urban development.

Nowadays urban economics and complexity theories are two main ways to research issues of urban development. However, new paradigms based on complexity theories have been gradually developed since 1980 and produced ideas different from the paradigms which are based on traditional urban economics, such as emergence, holism, non-linear dynamic world views, and analytical methods. This study is intended to explore the relationship between the two paradigms and how to reproduce spatial urban systems and urban complexity phenomena on the basis of the results which have been developed.

Also, in the past research, the urban power law phenomena have been repeatedly observed in the processes of urban development, such as the empirical research by Zipf (1949) and Rosen & Resnick (1980). The urban power law phenomena are aimed at studying some quality possessed by the scale structure and population spatial distribution of urban development. On the basis of economic theories, traditional economic paradigms seeked the regularities gathered and formed by such urban scales, such as Christaller (1933). However, complexity science paradigms interpreted them from the perspectives of complexity theories, such as Chen & Zhou (2003). According to Anas (1998), this study combines agglomeration economic model of traditional urban economics with non-economic model (e.g. increasing return) of complexity theories, building a two-dimension spatial model of a simple 3x3 grid and attempting to combine the viewpoints of economic theories with complexity system ideas.

Based on the random growth process of Arthur’s (1990a; 2000) increasing returns and non-linear path-dependent idea, the 3x3 grid model of this study was experimented. The results of calculations showed: (1) that the probabilistic expected values formed by different urban spatial clusters and the resulting power law coefficients were consistent with the empirical findings, with high frequencies associated with small clusters; (2) that the power law coefficients based on increasing returns tended to be closer to real urban systems (the slopes derived from the rank-size rule) in comparison with the non-increasing returns cases; (3) that among the three models: the 3x3 grid model designed in the research, the experiment of non-linear Polya process (Chen, 2004), and computer simulation based on increasing returns (Yu, 2005), it was shown that Yu’s random growth model was the best in the case of spatial neighboring relationship and agglomerative effect (whose power law coefficient was closest to the ones found in empirical studies).

並列關鍵字

urban development theories ； urban economics ； complexity theories ； power law coefficient, ； increasing returns, ； 3x3 grid model.

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