On the conditions of validity of the value input-output model

The general aim of this paper is to show that even the simplest economic models may be largely trivial. One discusses how a value input-output model can be derived from a physical input-output model. In the physical input-output model, variables are physical quantities and prices and in the value input-output model, variables are quantities in currency units and price indexes. One demonstrates that the value model must be biperiodical, that is, never a-periodic as assumed by Leontief, and that price indexes must replace prices. Hence, two variants of the model are possible: (i) the operational model where the price indexes are the solution of the value model for the base year and (ii) the true model where the current prices solve the physical model for the current year. It is impossible to decide which model is the best. Both models diverge generally unless some strong hypotheses are made: stability of the vertically integrated physical coefficients of labor, or even stability of the physical structure itself. Working on an aperiodic value model is not innocent even if virtually all scholars and practitioners use to do by operational necessity. The results could be generalized to SAM models or to the SNA’s rectangular input-output model.