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<p>This paper examines whether the feedback control system model of Park and Yang (Int J Control Autom Syst 21(5):1407–1419, 2023) can capture the long-run decline in the profit rate under the constant elasticity of substitution (CES) production function. Marx’s law of the falling rate of profit (Capital, volume III (1894). Penguin Classics, London, 1991) states that technological progress tends to reduce profitability over time. Park and Yang (2023) developed a novel control system model to analyze this law under the Cobb–Douglas production function. Extending their framework, this paper derives a control law that maximizes the next-year profit rate under the CES function and evaluates the model using two US datasets. Across a wide range of substitution elasticities, the simulation results show that the profit rate continues to decline in the long run despite short-run profit-maximizing control. These results indicate that the control system model remains valid for the CES function and effectively captures the mechanism underlying Marx’s law.</p>

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Feedback Control Analysis for the Law of the Falling Rate of Profit with the CES Production Function

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Seong-Jin Park

摘要

This paper examines whether the feedback control system model of Park and Yang (Int J Control Autom Syst 21(5):1407–1419, 2023) can capture the long-run decline in the profit rate under the constant elasticity of substitution (CES) production function. Marx’s law of the falling rate of profit (Capital, volume III (1894). Penguin Classics, London, 1991) states that technological progress tends to reduce profitability over time. Park and Yang (2023) developed a novel control system model to analyze this law under the Cobb–Douglas production function. Extending their framework, this paper derives a control law that maximizes the next-year profit rate under the CES function and evaluates the model using two US datasets. Across a wide range of substitution elasticities, the simulation results show that the profit rate continues to decline in the long run despite short-run profit-maximizing control. These results indicate that the control system model remains valid for the CES function and effectively captures the mechanism underlying Marx’s law.