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Daniel Bernoulli appears to be the first who defined utility as a logarithmic function of wealth — in his famous paper on the measurement of risk in games “Specimen Theoriae Novae de Mensura Sortis” (1738).
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Sagoroff, S. Historical note on the application of mathematics in economics in Germany. Metrika 4, 78–81 (1961). https://doi.org/10.1007/BF02613868
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DOI: https://doi.org/10.1007/BF02613868