Victor Aguilar's Axiomatic Theory of Economics is 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 first-unit demand.
ii) It is negative monotonic; that is, u'(s) < 0.
iii) The integral of u(s) from zero to infinity is finite.
3) First-unit demand conforms to proportionate effect:
i)
Value changes each day by a proportion (called 1+j, with j denoting the day), of the previous day's value.
ii)
In the long run, the j's may be considered random as they are not directly related to each other nor are they uniquely a function of value.
iii)
The j's are taken from an unspecified distribution with a finite mean and a non-zero, finite variance.
Click here for a short (600-word) excerpt about Arrow, Debreu, Keen, Stiglitz and Kolmogorov.
Chapter Four of my book is , or if one skips the proofs, which are clearly demarcated. The other chapters are all . By comparison, a typical Journal of Economic Theory article is .
Click here for a comparison of the axiomatic systems of Aguilar, Debreu and Kolmogorov.
"I do not feel that this article [Arrow and Debreu, 1954] should go unchallenged before the readers of Econometrica. Otherwise, economists will accept its conclusions at face value and quote it in substantiation of other arguments, perhaps ones of economic policy affecting all of us."
Cecil Phipps
the only referee with a mathematical background
"We understand that it is very delicate to suppress any scientific criticism..."
Arrow and Debreu
refering to Phipps' criticism, which was suppressed
q and q 
j, with j denoting the day), of the previous day's value.
