Том 6

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Browsing Том 6 by Author "Morozov, Denys"

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    Balance function generated by limiting conditions
    (2023) Morozov, Denys
    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.