The Simple Analytics of Pure Public Good Provision
The Simple Analytics of Pure Public Good Provision
复制标题
纯粹公共物品供给的简单分析
作者：
R. Cornes;T. Sandler
数量出现在他的效用函数中。此外，外部性的存在实际上意味着第三种商品，其数量影响他的最佳选择和/或在任何情况下可达到的最大效用。因此，他的效用函数必须有三个参数。虽然这对这些问题的严格分析没有问题，但它确实使试图提供直观和几何的基本特征的解释变得复杂。纯公共产品模型激发了许多手段，每一种都有助于说明某些特定方面。鲍恩（Bowen，1943）和萨缪尔森（Samuelson，1955）指出，人们可以为每个个体绘制一条需求曲线或边际替代率曲线，它们的垂直总和是与帕累托最优状态下公共物品和私人物品之间的边际转化率相等的相关对象。这个简单的结构假设了一个给定的分配或一个特殊的偏好类别，以保证最优公共产品的提供是独立于分配的。同样，约翰森（Johansen，1963）也对林达尔均衡进行了图解处理，该均衡同样对收入再分配敏感。McGuire和Aaron（1969）使用了另一种图表来分析当可用政策工具的范围--具体而言，进行一次性收入转移和选择个人成本份额的能力--有限时，公共产品的有效提供。Pauly（1970）在一个类似的图中描述了无效率的均衡分配;然而，Pauly的图不允许在均衡和最优之间进行简单或直接的比较。阿特金森和斯蒂格利茨（Atkinson and Stiglitz，1980，p.507）的处理方法也是如此，他们使用的是两部分图。其他现代的论述，如Boadway（1979），在他们的讨论中避免了这一点上的图表。本文件提供了一个相对简单的图，它允许一个描绘的正统纳什均衡和帕累托最优配置在一个纯公共产品的经济集进行了彻底的讨论。这张图也可以简单地表示这种经济中的林达尔均衡。在简单的两个人的例子中，我们的图表类似于私人物品交换经济的埃奇沃思盒处理，在这个特殊情况下，它可以容纳偏好或禀赋的差异而不复杂。对于两个以上人口的经济体，如果假设消费者的品味和禀赋相同，那么该图仍然可以使用。在私人商品经济中，
quantities appear in his utility function. Also, the presence of the externality effectively implies a third commodity, the quantity of which influences his optimal choice and/or the maximum attainable utility in any situation. His utility function, therefore, must have three arguments. While this presents no problem for the rigorous analysis of such problems, it does complicate attempts to provide intuitive and geometric expositions of their essential features. The pure public goods model has inspired a number of devices, each useful in illustrating some particular aspect. Bowen (1943) and Samuelson (1955) noted that one could draw a demand, or marginal rate of substitution, curve for each individual, and that their vertical summation was the relevant object to equate with the marginal rate of transformation between public and private goods at a Pareto optimum. This simple construct assumed either a given distribution or a special class of preferences so as to guarantee that the optimal public goods provision was independent of distribution. Likewise, Johansen (1963) produced a graphical treatment of Lindahl equilibrium which again is generally sensitive to income redistribution. An alternative diagram has been used by McGuire and Aaron (1969) to analyse efficient public goods provision when the range of available policy instruments-specifically, the ability to make lump-sum income transfers and to choose individuals' cost shares-is limited. Pauly (1970) depicted inefficient equilibrium allocations in a similar diagram; however, Pauly's diagram does not permit an easy or direct comparison between equilibria and optima. This applies also to the treatment by Atkinson and Stiglitz (1980, p. 507), who used a two-part diagram. Other modern expositions, such as Boadway (1979), avoided diagrams at this point in their discussion. The present paper provides a thorough discussion of a relatively simple diagram which allows one to depict both the orthodox Nash equilibrium and the set of Pareto-optimal allocations in an economy with a pure public good. This diagram also allows for a simple representation of Lindahl equilibrium in such an economy. In the simple two person example, our diagram is analogous to the Edgeworth box treatment of a private goods exchange economy, and in this special case it can accommodate differences in preferences or endowments without complication. For an economy of more than two people, the diagram may still be used if the assumption of identical tastes and endowments across consumers is made. In a private goods economy with