報酬遞增理論對聚落體系影響之電腦模擬實驗

How Increasing Returns Mechanisms Form Settlement Systems: The Computer Experiments Method

于如陵(Ju-Ling Yu) ； 賴世剛(Shih-Kung Lai)

《建築與規劃學報》 4卷2期 (2003/12) Pp. 160-177

https://doi.org/10.30054/JAP.200312.0004

摘要

本文是探討報酬遞增理論對都市聚落體系空間分布之影響，試圖解釋何以都市聚落體系會形成冪次現象（Power law）。所謂的冪次法則是指事物出現的規模與頻率間的關係：物體的規模S和其出現次數，呈S(上標 –a)的比例關係，而形成一個自成組織的體系。在先前的研究中曾指出，根據報酬遞增理論所設計的電腦模擬中，在均質平面平面的假設下，會呈現出高度符合冪次現象的都市體系（于如陵，賴世剛，2001）。本文在此一基礎上，將模型的假設條件放寬，使其不限於均質平面，並加入遷移行為的考量，以求得更為真實及一般化的結論。 模擬結果顯示，在放寬假設後，所形成的聚落體系仍高度符合冪次現象，並不因加入遷移行為及非均質平面而改變。此外模擬結果顯示，考慮遷移行為後，往往有使大都市加速發展之趨勢。而非均質平面的模擬中則顯示，地理優勢只是影響都市區位的因素之一，小事件的發生加上報酬遞增效應，往往使得某些區位被鎖定而成為大型聚落，不能完全以區位優勢來解釋都市之發生。此發現與Arthur（1990）的廠商區位選擇理論的結論一致。另一方面，去除報酬遞增機制後的模擬結果顯示，其所形成之聚落體系之型態與真實世界相差甚遠。因此吾人猜測報酬遞增現象極可能是形成聚落體系冪次現象的機制之一，確切的結論需進一步理論上的驗證。

關鍵字

聚落體系 ； 報酬遞增 ； 冪次法則

並列摘要

The paper investigates the influences of increasing returns on the spatial distribution of urban settlement systems and attempts to interpret why urban settlement systems exhibit the power law distribution. The so called “power law” is referred to as the relationship between the scale and frequency of objects. That is, the number of objects whose sizes exceed S is proportional to S(superscript -a) , and then the system forms an organization automatically. The former research indicated that, based on the computer simulations designed on increasing returns, under the hypothesis of an uniform plane, the urban settlement systems highly conformed to the power law (Yu and Lai, 2001). Based on the ground, the paper relaxes the hypothetic restrictions of the model, so that it will not be constrained by the uniform plane and adds the consideration of migration behavior, for the purpose of making a more common, realistic conclusion.
The outcome of the simulations shows that, after the restrictions are relaxed, the settlement systems still closely conform to the power law; it does not change for adding migration behavior and non-uniform plane. Conclusive claims must be backed by deductive evidence. The result also shows that, after migration behavior is taken into consideration, it often accelerates the tendency of big cities growing up. While the outcome of the non-uniform plane indicates that geographical advantage is merely one of the factors that influences the location of a city, the occurrence of small events with the effect of increasing returns often make some locations become big settlements, so we can not totally use geographical advantage to interpret where the city will be formed. This finding is consistent with Arthur’s insight into the location choice theory of firms. On the other side, the result of simulation model show that after the mechanism of incresing returns is lifted, the formulated settlement system is far away from the real world. Therefore we argue that increasing returns would be one of the underlying mechanisms through which the power law relationship of urban settlement systems emerges.

並列關鍵字

Settlement Systems ； Increasing Returns ； Power Law

參考文獻

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