本研究以最適控制理論(optimal control theory)，嘗試建構兩種動態的經濟體系，包括不存在外部性的經濟體系與存在外部性的經濟體系，而每一種經濟體系各包含中央集權經濟模型與自由市場經濟兩個模型；中央集權經濟模型(社會規劃者)代表一種理想的經濟體，他追求的目標是社會的資源配置符合柏瑞圖效率條件，而自由市場經濟模型(由代表性生產者與代表性消費者所組成)則代表實際的經濟社會，他們的目標是追求個人最大利益。在建構模型時，同時考量了商品市場均衡條件、勞動市場均衡條件、資本的動態累積過程以及污染的動態累積過程；最後以最適控制方法來求解模型的一階條件，並比較兩種經濟模型的最適行為是否一致。
本研究證明當不存在污染外部性時，動態的自由市場經濟模型符合柏瑞圖效率條件；當存在污染外部性時，不考慮外部性的動態自由市場經濟模型將無法符合柏瑞圖效率條件；存在污染外部性時，將外部性內部化的自由市場經濟符合柏瑞圖效率條件，而且庇古稅在動態模型中依然是解決污染外部性有效的政策工具；最後探討本文中所有動態模型是否存在長期穩定均衡，以及長期均衡點的型態(馬鞍點)。

This research uses the optimal control theory to construct two kinds of dynamic economic systems, which are an economic system without externalities and with externalities. Within each economic system both the centralized economy model and the decentralized economy model are included. The centralized economy (a social planner) model representes a kind of ideal economy, and the goal what the social planner pursues is that the resource allocation of the society satisfies the Pareto Efficiency criteria. On the other hand, the decentralized economy model (consists of a representative producer and a representative consumer) demonstrates the real economy, where economic agents persue their own best interests. While constructing the models, goods market equilibrium, labors market equilibrium, the dynamic accumulation process of capital, and the dynamic accumulation course of pollution are under consideration. Then, I apply optimal control method to get the first order conditions, and compare these f.o.c’.s to verify whether they are unanimous.
This paper proves that when externalities of pollution does not exist in the dynamic economic system, the decentralized economy model can achieve the Pareto Efficiency. On the contrary, when externalities of pollution emerges in the dynamic economic system, the decentralized economy model cannot reach Pareto Efficiency. If the externalities of pollution is internalized by the dynamic decentralized economic system economy, it will coincide with Pareto Efficiency. Besides, Pigouvian tax is still an effective policy instrument. Finally, I discuss all dynamic models in this paper to find out whether there exists a long-term and stable steady state. I find stable steady state, saddle-point equilibria, do exist under certain restrictions.

誌謝 …………………………………………………………………………Ⅰ
摘要 …………………………………………………………………………Ⅱ
Abstract ……………………………………………………………………Ⅲ
目錄 …………………………………………………………………………Ⅳ
第一章 緒論 ………………………………………………………………1
第一節 研究動機與目的 ……………………………………………1
第二節 研究方法與研究架構 ………………………………………4
第二章 文獻回顧 …………………………………………………………6
第三章 最適成長與環境租稅管制之動態經濟模型 …………………12
第一節 模型建構與理論分析 ……………………………………12
不存在外部性的經濟體系 ……………………………………13
存在外部性的經濟體系 …………………………………………24
第二節 模型穩定性探討 …………………………………………35
第四章 結論與建議 ……………………………………………………38
附錄一 不存在外部性經濟體系的模型設定原理 ……………………40
附錄二 存在外部性經濟體系的模型設定原理 ………………………42
參考文獻 …………………………………………………………………44

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