A Theorem on the Recycling Paradox

Significant differences in the scale of metallurgical slag processing in different countries has led us to observe and formulate a paradox for a company that is engaged in recycling in the framework of a market economy. The theorem about the existence of the paradox of waste processing is formulated and proven. A mathematical model based on the original logarithmic one-factor production function of the enterprise is used. An analysis of the interaction of factors made it possible to determine the optimal conditions for the processing of production waste. The elasticity of the production function, the price of waste and the price of the product ratio predetermine the profitability for the company of processing either its own waste or those involved in the processing of waste from other enterprises on an agency basis. Based on the research results, options for building efficient circular industrial ecosystems are proposed. The institutional alternative is a market recycling company or an enterprise as part of a vertically integrated structure. An example is given from the practice of a large metallurgical plant.