Finding the Markets in the Math

This paper shows how to find competitive market prices in the pure mathematics of classical constrained optimization problems.

Numeraire Illusion: The Final Demise of the Kaldor-Hicks Principle

The result in this paper undercuts the major applications of the Kaldor-Hicks reasoning in the standard Chicago school (wealth maximization) of law and economics, cost–benefit analysis, policy analysis, and related parts of applied welfare economics.

Introduction to Property Theory

This is yet another unpublished paper to introduce property theory to various audiences, particularly economists.

Mathematics of Real Estate Appraisal

This paper on the math of real estate appraisal is my most downloaded paper on the SSRN site! Hence I might as well make it available here too. It is a long discourse on the mathematics of compounding and discounting.

Arbitrage Theory

This a reprint of an applied math paper connecting the notion of arbitrage and the Lagrange multipliers of mathematical economics. The paper has a simple application showing that a circular gear train (all in the same plane) with an odd number of gears is rigid (cannot move) like the graphic to the left.

Economics, Accounting, and Property Theory

This is my first book. In order to develop a mathematical model of the stocks and flows of property inside a firm, I first had to give a math model of the usual double-entry accounting for the stocks and flows of the scalar value, and then generalize it to vectors of property rights.

Arbitrage and Graphical Gridlock

The arbitrage-free law (or Kirchhoff’s voltage law) Recently I emailed a friend to complain when his organization used this 3 gear image as their logo. What was my complaint? Read on. The basic idea of arbitrage is to “get something for nothing” by trading commodities or currencies around some circle ending up with more than […]

Series-Parallel Duality: Part II: Financial arithmetic

In financial arithmetic and in the appraisal literature, it has been noticed that the basic formulas occur in pairs, one being the reciprocal of the other. This Part II of the series-parallel duality post shows that these reciprocal formulas are an example of the SP duality normally associated with electrical circuit theory.

Series-Parallel Duality: Part I: Combating Series Chauvinism

This post describes the duality between the usual (series) addition and the dual parallel addition. This duality is normally considered in electrical circuit theory and combinatorics, but it has a much wider applications. In Part I of this post, the focus is on developing series-parallel dual formulas—in contrast to the usual focus on formulas using only the series sum.

The Math of Double-Entry Bookkeeping: Part I (scalars)

Double-entry bookkeeping illustrates one of the most astonishing examples of intellectual insulation between disciplines—the very opposite of intellectual trespassing.