The Structural Limit of Production Chain Depth as a Defect of Scalar Monetary Architecture

The paper diagnoses a defect of scalar monetary architecture: a single stock serves both turnover and reserves, and a common erosion rate prevents components of different economic nature from having different rates. The consequence is a structural limit on the depth of the production chain; the limit is not removable by tuning parameters, but only by changing the architecture of money. Three results. (1)~Under non-negative consumption and a positive lower bound on the sum of the output growth rate and the inflation rate, the boundedness of the stock-to-output ratio is derived from the budget constraint rather than assumed. (2)~A counterexample is constructed: outside this condition the limit does not follow from the budget and constancy of the inflation rate --- the chain depth grows without bound, while the budget is satisfied and consumption equals output; going beyond the limit is accompanied by the decomposition of the stock into components with different dynamics, which is precisely what indicates the defect. (3)~It is shown that pooling of reserves does not eliminate the linear-in-depth growth of the required buffer under independent bounded shocks with positive mean. In the class of a bounded stock-to-output ratio, chain depth cannot grow over time. A companion paper shows that the transition to a vector architecture of money --- different components of the stock with different functions and different erosion rates --- removes the limit established here; thus the cycle proves: the restriction on chain length is a consequence of the prevailing monetary paradigm, not of production possibilities, and it is removable by a change of paradigm, not by tuning parameters within it.