We prove the existence of a Pareto optimal state of a society with non-binary personal preferences. To our knowledge, this is the weakest set of conditions under which the existence of a Pareto optimal state has been proven. In our theory everybody in society engages in maximization as a...

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...

We prove the existence of a Pareto optimal state of a society with non-binary personal preferences. To our knowledge, this is the weakest set of conditions under which the existence of a Pareto optimal state has been proven. In our theory everybody in society engages in maximization 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.

We prove the existence of a Pareto optimal state in a society with non-binary preferences.

Agency-based explanations of the great deprivation, contrasted with structure-based explanations, suffer not merely from the criticism of relying on irrational and irresponsible behavior of millions, including that of the most astute financial experts, but are also at a loss to explain why such...

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...

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...

This paper establishes relationships between static Nash equilibria and dynamic Markov perfect equilibria of tariff and quota retaliation games. In supermodular games where tariffs are strategic complements, the steady state of every, symmetric Markov perfect equilibrium must have lower tariffs...