The Consumption Value Chain A Hayekian Framework of Production, Distribution, and Crisis A purely theoretical framework

**Abstract** This paper develops a purely theoretical framework that quantifies the Hayekian triangle by extending the Austrian time structure of production to the consumption side. The central new object is the **consumption chain length** \(C\), defined as the expected number of recursive absorption steps of a unit of labor income across the household distribution. Its counterpart is the **production chain length** \(U\), the Wang measure of production roundaboutness; the two chains weight the same recursion differently—by probability on the consumption side and by value added on the production side. The paper provides a three-tier exact construction: a homogeneous closed form, a finite-rank closed form, and a continuous master version given by a Fredholm integral equation of the second kind. The three tiers are exact special cases of one another, not approximations. It then proves an axiom-level asymmetry theorem: under the axioms, the consumption chain length is bounded above (\( C<∞\); no upper-bound value is reported), whereas the production chain length is unbounded under rank-one technology (\( U=+∞\)). The asymmetry is structural and does not rest on adjustment speeds, frictions, or expectational errors, though its statement presupposes \(U\) in Wang’s sense. The interest rate is not an independent variable in this theory: it enters only through the debt-service share \(β\), and a falling rate moves \(β\) and the debt-to-income ratio \(f=D/Y\) together, shifting both the roundaboutness of manufacturing input (\(U\)) and the service share on the consumption side. The two chains therefore lengthen in the same direction, and the triangle becomes taller without becoming narrower—the geometric signature of credit-expansion (unsustainable) growth, distinguishable in geometry but not in data from time-preference-driven growth (taller and narrower). The paper further establishes an impossibility theorem: on the observation set \((r,C,U)\), a fall in time preference and credit expansion are pointwise indistinguishable; discrimination requires a fourth observable not cancelled by the difference \(β-γ\), such as the level of \(D/Y\), and this condition is necessary but not sufficient. Once debt has accumulated, the monetary gap and profit cross five boundary lines along the interest-rate axis, cutting the feasible domain into six phases. Under illustrative calibration, a rise in the rate drives manufacturing output \(47.38%\) below its pre-shock level at the trough and \(15.67%\) below it in the new steady state; the ratio of the two layers, \(3.02\), stays within \([2.897,3.057]\) (\(± 2.3%\)) across a four-dimensional sensitivity band, so the ratio is structural and may be cited, whereas the absolute drops are positional. The single crisis criterion is the utilization rate \(Y_M/Vcapacity<1\); the gap is merely an accounting value whose sign appears in both directions. The paper is purely theoretical: it reports no parameter estimates and no chain-length point readings, and all numerical content is illustrative calibration kept separate from within-axiom results. Empirical estimation of the framework’s two core objects—the distribution matrix and the landing kernel—is left as the interface for subsequent research.