The AXEC paradigm replaces conventional approaches. The significant distinction is that conventional approaches are subjective-behavioral while the AXEC paradigm is objective-structural. Behavioral second-guessing is trapped in a cul-de-sac, therefore it can safely be left behind.
An explanation of the first three axioms and their economic implications is, for a start, provided with the working paper
Geometrical Exposition of Structural Axiomatic Economics
Economics for Economists
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All working papers and published articles are available on the open access repository SSRN. Working papers are subject to continuous fine-tuning, stylistic improvements, and expansion. AXEC is an open project: just the elementary implications of the structural axioms are known at this early stage.
The elementary implications are adequate to refute conventional approaches on purely formal grounds. This settles matters because inconsistency is indefensible.
Behavior-free structural-systemic axioms in combination with the behavioral propensity function open up a comprehensive perspective, that is, establish a new economic paradigm.