turnpike theorem

简明释义

公路收费闸口理论

英英释义

例句

1.The application of the turnpike theorem in economic modeling helps predict optimal investment strategies over time.

在经济模型中应用turnpike theorem有助于预测长期的最佳投资策略。

2.By using the turnpike theorem, we can determine the most efficient path for resource allocation in our project.

通过使用turnpike theorem，我们可以确定项目中资源配置的最有效路径。

3.The researchers applied the turnpike theorem to optimize traffic flow in congested cities.

研究人员应用turnpike theorem优化拥堵城市的交通流量。

4.The turnpike theorem suggests that in many dynamic systems, the solution approaches a steady state as time progresses.

turnpike theorem表明在许多动态系统中，随着时间的推移，解会接近一个稳态。

5.In the context of urban planning, the turnpike theorem can guide the development of transportation networks.

在城市规划的背景下，turnpike theorem可以指导交通网络的发展。

作文

The concept of the turnpike theorem is a fascinating and crucial aspect of optimal control theory in economics. At its core, the turnpike theorem suggests that in an optimal growth model, the path taken by an economy will closely resemble a particular trajectory for most of the time, especially as it approaches a steady state. This theorem provides insights into how economies evolve over time and emphasizes the importance of certain paths in achieving long-term growth.To understand the implications of the turnpike theorem, we first need to consider what optimal control theory entails. It involves making decisions over time to maximize a certain objective, such as profit or utility. In economic models, this often translates to maximizing consumption or output while considering constraints like resources or technology. The turnpike theorem essentially states that regardless of the initial conditions of the economy, it will gravitate towards a path that resembles the optimal trajectory as time progresses.This phenomenon can be likened to a car traveling on a highway. Initially, the car may take various detours, but as it travels further, it finds itself on the main turnpike, which represents the most efficient route to its destination. Similarly, in economic terms, even if an economy starts off on a suboptimal path, it will eventually align itself with the optimal growth trajectory dictated by the turnpike theorem.One of the significant implications of the turnpike theorem is its application in policy-making. Policymakers can utilize the insights from this theorem to design strategies that encourage economies to follow optimal paths. By understanding the characteristics of the turnpike, they can implement measures that guide economic agents toward more efficient behaviors, ultimately leading to enhanced growth and welfare.However, it is essential to note that the turnpike theorem operates under certain assumptions. It assumes that the economy is closed and deterministic, meaning that there are no external shocks or uncertainties affecting its growth. In reality, economies are often subject to fluctuations and unexpected events that can divert them from the optimal path. Despite these limitations, the turnpike theorem remains a valuable tool for economists and policymakers alike.In conclusion, the turnpike theorem serves as a critical framework for understanding the dynamics of economic growth. Its assertion that economies tend to converge towards optimal paths over time offers significant insights into long-term planning and policy formulation. As we continue to study economic behavior, the turnpike theorem will undoubtedly remain a cornerstone of optimal control theory, guiding both theoretical research and practical applications in the field of economics.

“收费公路定理”这一概念是经济学中最优控制理论的一个迷人而关键的方面。其核心思想是，在一个最优增长模型中，经济体所采取的路径在大多数时间内将与特定轨迹非常相似，尤其是在接近稳态时。这个定理提供了关于经济如何随时间演变的见解，并强调了在实现长期增长时某些路径的重要性。为了理解“收费公路定理”的含义，我们首先需要考虑最优控制理论的内容。这涉及到在一定时间内做出决策，以最大化某一目标，例如利润或效用。在经济模型中，这通常转化为在考虑资源或技术等约束的情况下最大化消费或产出。“收费公路定理”本质上表明，无论经济的初始条件如何，它最终都会随着时间的推移而向一种类似于最优轨迹的路径靠拢。这种现象可以比作一辆汽车在高速公路上行驶。起初，汽车可能会走各种绕道，但随着行驶的进一步，它会发现自己在主干道上，这代表着通往目的地的最有效路线。类似地，在经济学中，即使一个经济体最初处于次优路径，它最终也会根据“收费公路定理”所规定的最优增长轨迹进行调整。“收费公路定理”的一个重要影响是其在政策制定中的应用。政策制定者可以利用该定理的见解来设计鼓励经济体遵循最优路径的策略。通过理解收费公路的特征，他们可以实施措施，引导经济主体朝着更高效的行为发展，从而最终促进增长和福利的提升。然而，必须注意的是，“收费公路定理”是在某些假设下运作的。它假设经济是封闭和确定性的，这意味着没有外部冲击或不确定性影响其增长。在现实中，经济常常受到波动和意外事件的影响，这可能使其偏离最优路径。尽管存在这些局限性，“收费公路定理”仍然是经济学家和政策制定者的重要工具。总之，“收费公路定理”作为理解经济增长动态的关键框架，其主张经济体随着时间的推移趋向于最优路径的观点，为长期规划和政策制定提供了重要的见解。随着我们继续研究经济行为，“收费公路定理”无疑将继续作为最优控制理论的基石，指导经济学领域的理论研究和实际应用。