Debreu (1959) made a half-hearted attempt to give an axiomatic foundation for the theory of economics. Unfortunately, by using grossly unrealistic assumptions, Debreu only succeeded in giving the axiomatic method a bad name. Keen writes:

It is almost superfluous to describe the core assumptions of Debreu’s model as unrealistic: a single point in time at which all production and exchange for all time is determined; a set of commodities – including those which will be produced in the distant future – which is known to all consumers; producers who know all the inputs that will ever be needed to produce their commodities; even a vision of “uncertainty” in which the possible states of the future are already known, so that certainty and uncertainty are formally identical. Yet even with these breathtaking dismissals of essential elements of the real world, Debreu’s model was rapidly shown to need additional restrictive assumptions (2001, p. 173).

O’Driscoll and Rizzo (1985) have also argued against the "perfect information" assumption, as has Stiglitz (2003b, p. 25):

In effect, the Arrow-Debreu model has identified the single set of assumptions under which markets were (Pareto) efficient. There had to be perfect information, or, more accurately, information (beliefs) could not be endogenous, they could not change either as a result of the actions of any individual or firm, including investments in information.

In sharp contrast to Debreu’s presentation of his assumptions, this author’s axioms are printed in plain language right up front before any theorems are deduced from them. There is no need for the prefatory phrase "In effect..." which Stiglitz found necessary because Debreu had been so opaque about his assumptions.

My assumptions are three:

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 (1999, pp. xxiii-xxiv).

Kolmogorov also prints his axioms in plain language right up front before any theorems are deduced from them:

Let E be a collection of elements which we shall call elementary events, and a set of subsets of E; the elements of the set will be called random events.

       I.    is a field of sets.

       II.   contains the set E.

       III. To each set A in is assigned a non-negative real number P(A).
             This number P(A) is called the probability of event A.

       IV.  P(E) equals 1.

       V.   If A and B have no elements in common, P(A+B) = P(A) + P(B)

A system of sets, , together with a definite assignment of numbers P(A), satisfying Axioms I-V,
is called a field of probability (1956, p. 2).

Here, Kolmogorov does not introduce any new terminology (“field” is a well-known math word) but is comfortable with the standard language of mathematicians. Debreu, however, is not comfortable with the standard language of economists but instead introduces his many assumptions by way of a long and idiosyncratic vocabulary list. Thus, by the time we have learned Debreu-speak, we have lost track of all our new assumptions about these familiar-sounding words. We have entered the land of “blackboard economics” without having ever passed a signpost with a concise five-point list of axioms like Kolmogorov provides.