The positive net profit space is a subspace of the transfer space

Friedrich, Thomas (2024): The positive net profit space is a subspace of the transfer space.

Abstract

The substrate concentration in source and sink and the combined net profit of the ensemble of both are the coordinates of the transfer space. Net profit is the difference of a non-linear benefit function and a linear cost function of the substrate concentration. The net profit of the ensemble, the sum of the net profit of source and sink, results in a surface within the transfer space. This surface is partially below zero, a negative net profit, and partially above zero, a positive net profit. Superadditivity appears when the surface with transfer is above the surface without transfer. Subadditivity is the revers situation. Superadditivity and subadditivity are independent of a positive or negative net profit. A positive net profit for the single parties and superadditivity for the ensemble would be optimal. I demonstrate that in a subspace of the transfer space (area III) a positive net profit for source and sink and superadditivity for the ensemble is possible. Two reservations have to be made: First, source has to be forced or deceived to give substrate beyond b=c, an attractor within the larger transfer space. Second, increased positive net profit for source and sink in symmetric ensembles is achieved on cost of superadditivity for the ensemble. The superadditive net profit of the ensemble by transfer and the individual net profit of source and sink are a trade-off within the subspace. If the individual net profit for source and sink is maxed out simultaneously, superadditivity is absent and additional transfers result in subadditivity in symmetric ensembles. Observing both limits of maximal net profit avoids subadditivity in area III. This is similar to the transfer space with the holding lines b=c. Such a pair of checklines is absent in area II.

• Item Type: MPRA Paper
• Language: English
• Keywords: source; sink; ensemble; transfer; superadditivity; subadditivity; force; deception; Solow-Swan model; trade-off; net profit; emergent cost; karoshi; greed; envy; contempt
• Subjects: Z - Other Special Topics > Z0 - General > Z00 - General

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