Monday, 3 November 2014

Ninomiya Golden path general equilibria

Wikipedia says 'In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state level or growth of consumption,[1] as for example in the Solow growth model. Although the concept can be found earlier in John von Neumann and Maurice Allais's works, the term is generally attributed to Edmund Phelps who wrote in 1961 that the Golden Rule "do unto others as you would have them do unto you" could be applied inter-generationally inside the model to arrive at some form of "optimum", or put simply "do unto future generations as we hope previous generations did unto us."[2]

However, by the Kirman & Koch refinement of the Sonnenschein Mantel Debreu result we know that no unique method of discriminating savings and consumption can exist except if there is
1) Rational Expectations
2) Aumann agreement based Hannan Consistency
in which case unique, but not neccessarily effectively computable equilibria exist. Call this the golden path general equilibrium. There may be a golden rule- but it is that of the Japanese Peasant Sage Ninomiya, not to mention a certain Jewish Carpenter who globalized the simple Mussar message- my spiritual needs require the satisfaction of the material needs of the other.
However, this can't be done by splitting populations into 'poor' and 'non poor'. On the contrary, it was because Ninomiya, not to mention Nund Reshi or the Nazarene, was himself poor that progress could be made.
Pity, but there it is.

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