限制条件产生的平衡功能

Denys Morozov
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This offers a theoretical basis for modeling and solving similar problems arising during practical economic activities.Two economies, Economy 1 and Economy 2, producing goods X and Y with linear Production Possibility Curve (PPC) graphs, are under consideration. The cost of producing one unit of good X relative to Y is denoted as R1 for Economy 1 and R2 for Economy 2. Exchange between economies occurs in a market, where the possible exchange is Δx units of X for Δy = Rmarket · Δx units of Y, and vice versa.If R1 is less than R2, Economy 1 specializes in the production of X, and Economy 2 specializes in Y, fostering mutually beneficial trade. For mutually beneficial exchange on the market with a price Rmarket, it is necessary and sufficient that R1 ≤ Rmarket ≤ R2.The article also explores the concept of a fair exchange price, specifying conditions for symmetry, reciprocity, and scale invariance. 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摘要

本文对描述两个市场之间相互作用的价格函数形成的内在制约因素进行了分析。文章定义了构建价格函数时考虑的关键因素。通过分析这些制约因素及其对市场互动的影响,提供了价格函数的计算公式。这种方法不仅揭示了形成价格函数的自然制约因素的本质,还为两个市场互动过程中形成公平交换价格的谈判提供了背景基础。经济 1 和经济 2 是两个经济体,分别生产具有线性生产可能性曲线(PPC)图的商品 X 和 Y。经济之间的交换在市场上进行,可能的交换是 Δx 单位的 X 换取 Δy = Rmarket - Δx 单位的 Y,反之亦然。如果 R1 小于 R2,则经济 1 专门生产 X,经济 2 专门生产 Y,从而促进互利贸易。文章还探讨了公平交换价格的概念,明确了对称性、互惠性和规模不变性的条件。值得注意的是,文章指出满足这些条件的唯一解是 f(R1,R2) = √ R1 - R2。在平衡交换的情况下,各经济体获得的每单位所购商品的利润相等,平衡交换价格 Rmarket[balance] 被确定为 Rmarket = √ R1 - R2。在所提供的 R1 = 2 和 R2 = 8 的例子中,文章研究了 Rmarket 的互利区间,并计算了平衡和公平的交换价格。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Balance function generated by limiting conditions
This article conducts an analysis of the inherent constraints governing the formation of the price function that describes the interaction between two markets. The research not only identifies these constraints but also obtains an explicit form of the specified function.The key factors considered in constructing the price function are defined in the article. Through analyzing these constraints and their impact on market interaction, a formula for the price function is provided. This approach not only reveals the essence of natural constraints in forming the price function but also provides a contextual foundation for negotiations shaping a fair exchange price for the interaction process between two markets. This offers a theoretical basis for modeling and solving similar problems arising during practical economic activities.Two economies, Economy 1 and Economy 2, producing goods X and Y with linear Production Possibility Curve (PPC) graphs, are under consideration. The cost of producing one unit of good X relative to Y is denoted as R1 for Economy 1 and R2 for Economy 2. Exchange between economies occurs in a market, where the possible exchange is Δx units of X for Δy = Rmarket · Δx units of Y, and vice versa.If R1 is less than R2, Economy 1 specializes in the production of X, and Economy 2 specializes in Y, fostering mutually beneficial trade. For mutually beneficial exchange on the market with a price Rmarket, it is necessary and sufficient that R1 ≤ Rmarket ≤ R2.The article also explores the concept of a fair exchange price, specifying conditions for symmetry, reciprocity, and scale invariance. Notably, it indicates that the unique solution satisfying these conditions is f(R1,R2) = √ R1 · R2.In the context of balanced exchange, where economies gain equal profit per unit of the acquired good, the balanced exchange price Rmarket[balance] is determined as Rmarket = √ R1 · R2. This serves as a fair price, meeting the aforementioned conditions of symmetry, reciprocity, and scale invariance.In the provided example with R1 = 2 and R2 = 8, the article examines the mutually beneficial interval for Rmarket and computes the balanced and fair exchange price.
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