Proof of the law of diminishing returns

@article{Shephard1970ProofOT,
  title={Proof of the law of diminishing returns},
  author={Ronald W. Shephard},
  journal={Zeitschrift f{\"u}r National{\"o}konomie},
  year={1970},
  volume={30},
  pages={7-34}
}
  • R. Shephard
  • Published 1970
  • Mathematics
  • Zeitschrift für Nationalökonomie
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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