Mathematical Foundations for the Economy of Giving

Abstract: This paper shows how we can build a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we are able to redefine concepts like account balance, yield curve and the law of diminishing returns. The model provides us with a result that expresses how people have a structural preference for one recipient over the other regardless the actual account balance. Hence a building block in the social fabric of a community. Finally, a fundamental theorem is presented to show how suppliers and recipients use their account balance in order to reach an equilibrium in the exchange of goods much like the traditional balance between supply and demand.