On the density of nice Friedmans

A Friedman number is a positive integer which is the result of an expression combining all of its own digits by use of the four basic operations, exponentiation and digit concatenation. A "nice" Friedman number is a Friedman number for which the expression constructing the number from its own digits can be represented with the original order of the digits unchanged. One of the fundamental questions regarding Friedman numbers, and particularly regarding nice Friedman numbers, is how common they are among the integers. In this paper, we prove that nice Friedman numbers have density 1, when considered in binary, ternary or base four.Comment: 6 page

Oscillating Friedman Cosmology

The non-singular, oscillating Friedman cosmology within the framework of General Relativity is considered. The general oscillatory solution given in terms of elliptic functions and the conditions for its existence are discussed. It is shown that the wall-like-matter and the small, but negative cosmological constant are required for oscillations. The oscillations can , in principle, be deep enough to allow standard hot universe processes like recombination and nucleosynthesis. It is shown that the wall-like-matter and string-like-matter can be interpreted as scalar fields with some potentials. This may give another candidate for the dark matter which may be compatible with observational data. For an exact elementary oscillatory solution it is shown that the associated scalar field potential is oscillating as well.Comment: Latex file, 27 pages, figures available on reques

Optimality of the Friedman Rule in Overlapping Generations Model with Spatial Separation

Recent papers suggest that when intermediation is analyzed seriously, the Friedman rule does not maximize social welfare in overlapping generations model in which money is valued because of spatial separation and limited communication. These papers emphasize a trade-off between productive efficiency and risk sharing. We show financial intermediation or a trade-off between productive efficiency and risk sharing are neither necessary nor sufficient for that result. We give conditions under which the Friedman rule maximizes social welfare and show any feasible allocation such that money grows faster than the Friedman rule is Pareto dominated by a feasible allocation with the Friedman rule. The key to the results is the ability to make intergenerational transfers.monetary policy, Friedman rule, fiat money

From Keynes to Friedman via Mints: Resolving the Dispute over the Quantity Theory Oral Tradition

The Keynes Before Keynes Milton Friedman (chapter 2 [1956], 3-4) asserted that “Chicago was one of the few academic centres at which the quantity theory continued to be a central and vigorous part of the oral tradition throughout the 1930’s and 1940’s”. Friedman sought to “nurture” the revival of the quantity theory by linking it to this Chicago “oral tradition”. According to Friedman the “flavor” of this oral tradition was captured in a model in which the quantity theory was “in the first instance a theory of the demand for money”. Friedman added that to “the best of my knowledge no systematic statement of this theory as developed at Chicago exists, though much of it can be read between the lines of [Henry] Simons’ and [Lloyd] Mints’s writings”. He also enlisted the names of Frank Knight and Jacob Viner in support of his assertion. ISBN: 185196767

Milton and money stock control

Milton Friedman Luncheon, University of Missouri-Columbia, Columbia, Mo., July 31, 2007Money supply ; Friedman, Milton

Response to Friedman

An abstract for this article is not available.Monetary policy

A Godel-Friedman cosmology?

Based on the mathematical similarity between the Friedman open metric and Godel's metric in the case of nearby distances, we investigate a new scenario for the Universe's evolution, where the present Friedman universe originates from a primordial Godel universe by a phase transition during which the cosmological constant vanishes. Using Hubble's constant and the present matter density as input, we show that the radius and density of the primordial Godel universe are close, in order of magnitude, to the present values, and that the time of expansion coincides with the age of the Universe in the standard Friedman model. In addition, the conservation of angular momentum provides, in this context, a possible origin for the rotation of galaxies, leading to a relation between the masses and spins corroborated by observational data.Comment: Extended version, accepted for publication in Physical Review