Control and Crisis in a City Seen as a Reactor of Economic Transactions

The distribution of persons in each economy by their income is similar to the Maxwell-Boltzmann equilibrium distribution encountered in various physical systems. The transactions the persons are making to buy things that make them survive (in all sort of ways) are making them ‘poorer’, diminishing the amount of money they have. The ‘work and get paid’ type of transactions are rebuilding the financial capacity of the persons. Describing this process as a diffusion equation, in a cylindrical geometry, results in a Bessel function J0(r) solution, which matches the density distribution of persons in Paris (as a typical circular pattern city). Moreover, a simple equation for the dynamic behavior of a city, on which a 365 days period is imposed, results in one week as the time after which persons have to be paid to restart transactions, in the case of prompt pay. Thus, the extension of the basic model of the city as a reactor of economic transactions, for the cases of control through insertion or absorption of money, lead to the description of the crisis with a strikingly good accuracy for the case of Romania in 2009. Moreover, considering the prompt and delayed pay case gives a change in the average time to replenish financial resources of persons from 7 to 30 days. Using neutron physics methods in describing the economic transactions environment opens an alternative view on the forecasting models of economic systems’ behavior, and shows that the geographical dimension of a city is determined by the economic transaction behavior/environment in that city.