We prove the existence of a Pareto optimal state of a finite society that has socially differentiated persons, each with non-binary personal preferences that quasi-order a finite set of alternatives. Everybody engages in a volitional act of choice by maximization of non-binary preferences. As a...

In this work we construct a lower bound for an odd perfect number in terms of the number of its distinct prime factors. We further generalize the formula for any natural number for which the number of its distinct prime factors is known.

As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is called the special prime. In this work we show that p≥13 and if q∈{3,5} and q|n then either gcd⁡(q,σ(m^2 ))=1 or gcd⁡(q,σ(p^α ))=1.

Ken Arrow (1998) asks, “What has economics to say about racial discrimination?” He replies – entirely correctly – that racial “segregation within an industry – that is, firms with either all black or all white labor forces” – may be explained by economic theory, but “the...

Diverse identities, some socially shared, arise from a person’s affiliation with multiple overlapping communities, which are non-disjoint subsets of persons in society. I prove that identification of each individual with binary preferences or their utility function representation, commonplace...

A country’s production possibility frontier or PPF is defined as the boundary of its economy’s production set in the net output space for a given technology and fixed quantities of primary factors of production. In general equilibrium theory, exogenous changes in technology or primary-factor...

In his Inquiry into the Nature and Causes of the Wealth of Nations Adam Smith (1776) considered the phenomenon of division of labor so enormously significant for the creation of a nation’s wealth that he devoted the first three chapters of his book to an investigation of this process. This is...

The American economy has undergone a dramatic structural change in the first decade of the 21st Century. The real-economy causes of this transformation, and their expression via the real estate market and its financial derivatives’ market, and their final manifestation in world financial...

Jointly with Erkko Etula, Paul Samuelson [2006] claims that the “Leontief – Sraffa matrix equations for input/output must obey constant returns to scale”. However, in an unrelated work, Amartya Sen [2003] claims that Sraffa’s [1960] “analysis does not need any assumption of constant...

This paper examines some of the consequences for economic theory of the replacement of binary personal preferences by non-binary personal preferences in an Arrow-Debreu society as in Debreu (1959), and reaches the conclusion that there is both much damage to existing theory and greater...