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nvariants of this type might lay the foundations for an entirely novel type of theory." Schumpeter (1949, p. 155), discussing the Pareto law — via [Gabaix 2009] This paper introduces some mathematical and simulation models and supports these models with various theoretical ideas from economics, mathem
he details of income and wealth distributions have rarely been studied in mainstream theoretical economics, a notable and important exception being Champernowne. Champernowne was a highly gifted mathematician who was diverted into economics, he was the first person to bring a statistical mechanical approach
a particular focus of attention, as its form gives rise to constant shares of returns to labour and capital. (I am somewhat reluctant to criticise Gabaix, as he is one of the few economists who has recognised the importance of power-laws and other 'anomalous' invariants in economics. However his quote
ater in economics, this area has attracted physicists and statistical mathematicians and engineers in significant numbers since at least the work of Champernowne. The reason is simple; to a statistical physicist, economics is obviously a multi-body phenomenon. It is messy. There are millions of agents in a t
butions, and the split of the returns from labour and capital are all long-standing 'anomalies' within economics. Economists such as Schumpeter and Gabaix have noted these regularities [Gabaix 2009]. Why almost all other economists, even heterodox economists such as Gallegati et al, have shown such dis
lots of boundary conditions, may be simple enough to be tractable to a traditional statistical mechanical analysis on the lines of Dewar, or indeed Champernowne. Before moving into further discussion I would first like to follow the maths through a little more. I would like to do two things. Firstly I would
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