Lagrange Principle of Wealth Distribution

Abstarct

The Lagrange principle L = f + λg → maximum! is used to maximize a function f(x) under a constraint g(x). Economists regard f(x) = U as a rational production function, which has to be maximized under the constraint of prices g(x). In physics f(x) = lnP is regarded as entropy of a stochastic system, which has to be maximized under constraint of energy g(x). In the discussion of wealth distribution it may be demonstrated that both aspects will apply. The stochastic aspect of physics leads to a Boltzmann distribution of wealth, which applies to the majority of the less affluent population. The rational approach of economics leads to a Pareto distribution, which applies to the minority of the super rich. The boundary corresponds to an economic phase transition similar to the liquid - gas transition in physical systems.