| Abstract: | Many recent models of trade dynamics use the simple idea of wealth exchanges among
economic agents in order to obtain a stable or equilibrium distribution of wealth among
the agents. In particular, a plain analogy compares the wealth in a society with the
energy in a physical system, and the trade between agents to the energy exchange between
molecules during collisions. In physical systems, the energy exchange among molecules
leads to a state of equipartition of the energy and to an equilibrium
situation where the entropy is a maximum. On the other hand, in a large class of exchange
models, the system converges to a very unequal condensed state, where one
or a few agents concentrate all the wealth of the society while the wide majority of
agents shares zero or almost zero fraction of the wealth. So, in those economic systems a
minimum entropy state is attained. We propose here an analytical model where we
investigate the effects of a particular class of economic exchanges that minimize the
entropy. By solving the model we discuss the conditions that can drive the system to a
state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of
wealth. |
