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Proof of the law of diminishing returns

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Abstract

Based on a general mathematical model of a technology, implying certain properties for the production function, weak and strong forms of a physical law of diminishing returns are derived. It is also shown that the classical forms of this law hold if the technology is homogeneous (degree one) and the production possibility sets of the technology are strictly convex, but the latter property violates an essential property of a technology, namely that these sets have bounded efficient subsets.

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Dedicated to my friend Oskar Morgenstern who called this issue to my attention and urged me to work on it.

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Shephard, R.W. Proof of the law of diminishing returns. Zeitschr. f. Nationalökonomie 30, 7–34 (1970). https://doi.org/10.1007/BF01289990

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