Subject. This article deals with the problem of constructing a Leontief's input–output matrix. Objectives. The article aims to determine the rules for constructing a Leontief's input–output matrix on the basis of data on production time and quantity of product output. Methods. For the study, I used the methods of logical and mathematical analyses. Results. The article formulates the rules for constructing a Leontief's input–output matrix, taking into account differences in the time of production, quantity of output, as well as the conditions for the reproduction of the resources expended. It summarizes these rules for the J. von Neumann model. Conclusions. The proposed approach to the analysis of the material mechanism of economic reproduction defines the relationship between the quantitative and cost characteristics of the production and consumption of products and resources. This relationship opens up new opportunities for the application of input–output models to create simple and accurate algorithms for identifying and predicting the macroeconomic trends.
Keywords: Leontief's model, inter-industry balance, input–output matrix, reproduction, theory of value
Pospelov I.G. [Modeling Russian economy in the crisis period]. Voprosy Ekonomiki, 2009, no. 11, pp. 50–75. (In Russ.) URL: Link
Leontief W.W. Khozyaistvo kak krugooborot. V kn.: Izbrannye proizvedeniya: v 3 t. T. 3. Izbrannye stat'i [The Economy as a Circular Flow. In: Selected works: in 3 vol. Vol. 3. Selected articles]. Moscow, Ekonomika Publ., 2007, pp. 24–92.
Samuelson P.A. Leontief's “The Economy as a Circular Flow”: An Introduction. Structural Change and Economic Dynamics, 1991, vol. 2, iss. 1, pp. 177–179. URL: Link90011-G
Vorontsovskii A.V. [W.W. Leontief – The outstanding economist of the 20th century]. Vestnik Sankt-Peterburgskogo universiteta. Ekonomika = St. Petersburg University Journal of Economic Studies, 2007, no. 1, pp. 3–10. URL: Link (In Russ.)
Baranov А.О., Pavlov V.N.,Tagaeva T.O., Slepenkova Yu.M. [Construction and use of the regional input-output model with environmental and economic development blocks]. Mir ekonomiki i upravleniya = World of Economics and Management, 2020, vol. 20, iss. 3, pp. 27–47. URL: Link (In Russ.)
Kurz H.D., Salvadori N. [Input-output analysis from a wider perspective: a comparison of the early works of W. Leontief and P. Sraffa]. Vestnik Sankt-Peterburgskogo universiteta. Ekonomika = St. Petersburg University Journal of Economic Studies, 2007, no. 2, pp. 3–21. URL: Link (In Russ.)
Klyukin P.N. [Evolution of the circular flow theory within the 20th century and its present-day perspectives]. Вiсник Киiвського нацiонального унiверситету iм. Тараса Шевченка. Серiя: Економiка, 2013, no. 146, pp. 42–46. URL: Link (In Russ.)
Quesnay F. Ochevidnost'. V kn.: Fiziokraty. Izbrannye ekonomicheskie proizvedeniya [Évidence. In: The Physiocrats. Selected economic works]. Moscow, Eksmo Publ., 2008, pp. 45–86.
Sraffa P. Proizvodstvo tovarov posredstvom tovarov (prelyudiya k kritike ekonomicheskoi teorii) [Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory]. Moscow, YUNITI Publ., 1999, 159 p.
Dmitriev V.K. Ekonomicheskie ocherki [Economic Essays on Value, Competition and Utility]. Moscow, Higher School of Economics Publ., 2001, 580 p.
Kurz H.D. [Marx and the “law of value”: Critical appraisal on the occasion of his 200th birth anniversary]. Voprosy Ekonomiki, 2018, no. 11, pp. 27–49. (In Russ.) URL: Link
Bodrikov M.V. [Sraffian Theory of Value: An Intermediate Stage of the Return to the Classics]. Terra Economicus, 2018, vol. 16, no. 2, pp. 46–74. (In Russ.) URL: Link
Rassokha A.V., Shananin A.A. [Inverse problems of the analysis of input-output balances]. Matematicheskoe modelirovanie = Mathematical Models and Computer Simulations, 2021, vol. 33, no. 3, pp. 39–58. (In Russ.) URL: Link
Al-Salih R., Habeeb A., Laith W.H. A Quantum Calculus Analogue of Dynamic Leontief Production Model with Linear Objective Function. Journal of Physics: Conference Series, 2019, vol. 1234. URL: Link
Kramarov S.O., Pelikhov N.V., Sakharova L.V., Khramov V.V. [Modification of the Leontief model for description of regional economic clusters]. Vestnik Universiteta, 2019, no. 12, pp. 78–86. (In Russ.) URL: Link
Pavlova N.G. [Study of the continuous-time open dynamic Leontief model as a linear dynamical control system]. Differentsial'nye uravneniya = Differential Equation, 2019, vol. 55, no. 1, pp. 111–116. (In Russ.)
Von Neumann J. А Model of General Economic Equilibrium. The Review of Economic Studies, 1945, no. 13, iss. 1, pp. 1–9. URL: Link