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October 19th, 2015, 06:05 PM  #1 
Member Joined: Oct 2015 From: Arizona Posts: 57 Thanks: 0 Math Focus: Analysis  Axiomatic Economics
I have a degree in mathematics. I wrote a book about economics (Axiomatic Theory of Economics, ISBN# 1560722967) in 1999 in which I propose a new theory of economics based on three axioms: 1) One's value scale is totally (linearly) ordered: i) Transitive; p <= q and q <= r imply p <= r ii) Reflexive; p <= p iii) Antisymetric; p <= q and q <= p imply p = q iv) Total; p <= q or q <= p 2) Marginal (diminishing) utility, u(s), is such that: i) It is independent of firstunit demand. ii) It is negative monotonic; that is, u'(s) < 0. iii) The integral of u(s) from zero to infinity is finite. 3) Firstunit demand conforms to proportionate effect: i) Value changes each day by a proportion (called 1+Ej, with j denoting the day), of the previous day's value. (E means epsilon) ii) In the long run, the Ej's may be considered random as they are not directly related to each other nor are they uniquely a function of value. iii) The Ej's are taken from an unspecified distribution with a finite mean and a nonzero, finite variance. 
October 20th, 2015, 03:54 PM  #2 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 573 Thanks: 79 
How much calculus is needed to understand your book? Axiomatic Theory of Economics by Victor Aguilar  9781560722960  Hardcover  Barnes & Noble says it assumes three semesters of calculus. How much of the book requires the reader to know functions with more than one independent variable?

October 20th, 2015, 06:13 PM  #3  
Member Joined: Oct 2015 From: Arizona Posts: 57 Thanks: 0 Math Focus: Analysis  Simplified Exposition of Axiomatic Economics Quote:
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October 20th, 2015, 09:14 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Very interesting! Perhaps you should post on the Economics forum where you might get more attention. (FWIW this book is relevant to my interests, as I studied math/econ in college and have maintained an interest in axiomatic economics, e.g. Arrow's Theorem and its ilk.) I went to your site and started to read some of the material there, though I only finished a few pages. Your first two axioms, though not completely obvious, are at least fairly reasonable and intuitive. I'm not so sure about the last one. Do you have any thoughts on why we should accept this axiom? 
October 21st, 2015, 11:32 AM  #5  
Member Joined: Oct 2015 From: Arizona Posts: 57 Thanks: 0 Math Focus: Analysis  Quote:
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