不定期海運市場動態均衡與系統安定分析──最適控制理論之應用

ANALYSIS OF DYNAMIC EQUILIBRIUM AND SYSTEM STABILITY FOR THE INTERNATIONAL TRAMP SHIPPING MARKET－APPLICATION OF OPTIMAL CONTROL THEORY

本研究旨在建構一涵蓋船舶與貨運市場之動態經濟模型，並利用最適控制理論，來探討不定期海運市場之動態均衡與系統安定性。有別於Beenstock 模型之馬鞍點均衡模型，經本研究模型可推導得：不定期海運市場乃是建立在船舶與貨運市場皆達恆定狀態下，具收斂性之穩定均衡市場。再者，本研究亦利用線性化安定分析，來了解於均衡點鄰域之局部穩定性，並得知：當不定期海運市場失衡時，整體市場回復均衡之路徑與速度，主要是受船舶報廢率與租傭率所影響。而當前者越遲緩或後者越敏感時，市場波動則將越趨安定且回復均衡之速度亦越快速。反之，則較易呈現過度反應之不安定收斂體系。另外，不同於Beenstock模型，本研究模型亦顯示：即使在不具預期心理情況下，不定期海運市場仍會出現過度反應現象。最後，經由比較靜態分析得知：新船數量增加將降低均衡運價水準，但對船舶存量之衝擊則不明確。相對的，油價上揚與運輸需求增加，皆會帶領運價水準與船舶存量同時上揚。

By applying the optimal control theory, in this paper, a dynamic economicmodel reflecting the inter-connected activities among new-building, secondhand,scrapping and freight markets has been developed to demonstrate the dynamicequilibrium and stability of system convergence in the international trampshipping market. By satisfying the steady state conditions in ship and freightmarkets, the model developed in this paper has definitely shown that theinternational shipping market is a stably convergent equilibrium market,regardless of the saddle point equilibrium outcome presented in the Beenstockmodel. By following the outcome of linearization stability analysis which focuseson investigating the local stability around the neighboring area of theequilibrium point, the model suggests that the rate of scrapping and rate ofchartering ships have played critical roles in determining the adjustment speedand the path of recovering from the disequilibrium point to the equilibrium point.As the scrapping rate is more sluggish to the freight variations, the recovery ofthe shipping market disequilibrium will become more stable and quick to adjustback to its equilibrium. This paper has also illustrated that the fright level andstock of ships may have presented an overshot response to the market shock,even if the necessary condition of rational expectation to ship price formulatedin the Beenstock model is not applied in this model. By following thecomparative static analysis, furthermore, the model has also shown that theincrease in new ships delivered will bring a negative effect on the optimalequilibrium freight level, but an ambiguous effect on the optimal stock of ship. Incontrast, the increase in fuel price and transportation demand will increase theoptimal freight level and stock of ship.