THE CITIES: REACTORS OF ECONOMIC TRANSACTIONS

Abstract

The distribution of persons in each economy by their incomes 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’, as they diminish 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). The analysis of the decrease in income shows a saving/spending behavior function which saturates around 15% - 20% of the total income. This is a possible explanation of the frequent savings value of 15%-22% of GDP found in various economies. 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. The transaction cross section s is shown to have a “1/income” behavior, being a measure of the capability to make transactions, proportional to the probability of enterprises to have an income greater than a given value – this behavior has recently been shown to happen in various economies and it is known as the Zipf’s law. Using neutron physics methods in describing the economic transactions environment opens an alternative view on the forecasting models of an economic system’s behavior, and shows that the geographical dimension of a city is determined by the economic transaction behavior/environment in that city.