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Demand-Driven and Supply-Sided Input–Output Models

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Abstract

In the demand-driven open input–output model, output is determined by final demand, given the production technology in every industry. On the contrary, in the supply-sided version, value added determines the level of output and producers must induce sales in order to achieve a desired level of income. This latter version of the model has been criticised and even rejected on its implausibility, its difficult interpretation and its bizarre implications, among other aspects. This paper argues that the supply-side model is not logically, mathematically or otherwise at odds with Leontief’s arguments. Rejection of the model is a matter of theoretical reading.

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Notes

  1. Forward linkages measure the relative capacity of each sector to induce the use of its output as input by other producers; backward linkages measure the relative ability of each sector to use other sectors’ output as inputs (Bulmer-Thomas, 1982).

  2. Using Ghosh’s original notation.

  3. Matrices A and E are similar if matrix X exists, such that XA = XE, which means that E = X−1AX; for example, X = <x>, the diagonal matrix of sectoral output (Hadley 1969).

  4. L and H are said dominant diagonal matrices and among some other properties, they are non-singular (Takayama 1985).

  5. “… the equivalence of the supply-driven input–output model and the Leontief price model can also be shown in another, surprisingly simple manner. Given the assumption of fixed quantities, the Leontief price model calculates the new price ratios for a given new value-added vector (v1′) as π′= v1′xo (I − A)−l. The element πi expresses the new price in terms of the old price for good i; πi is thus a price index. The new output values (xi′) are obtained by revaluing the old outputs in their new prices. In other words, xi′ = π′\(\hat{x}\)0. Post multiplying both sides … with \(\hat{x}\)0 and using B0 = \(\hat{x}\) −10 A0\(\hat{x}\)0 yields x1′ = v1′ (I − B0)−1, which is exactly the supply-driven input-model…” (Dietzenbacher 1997, p. 634). In his notation, B = E the distribution coefficients matrix.

  6. To the best of our knowledge, Leontief did not adhere explicitly to any theory of value and avoided such discussion when reconsidering both Walras’ and Marx’s theories (Leontief 1937, 1938).

  7. Given any matrices A and B, B B—1 = I, the identity matrix; therefore, BAB—1 = A (Harary 1969).

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Acknowledgements

We are indebted to Prof. Dr. Joerg Beutel for useful comments and observations to an earlier version of this paper. Two anonymous referees have made valuable suggestions to improve this paper. We assume responsibility for all the remaining mistakes.

Funding

Financial support to conduct our research work by PAPIIT (UNAM) Project IN301018 is gratefully acknowledged, Dr. Marquez is also grateful to Programa de Becas Posdoctorales en la UNAM, Becario del Instituto de Investigaciones Económicas.

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  1. Facultad de Economía, Universidad Nacional Autónoma de México (UNAM), Circuito Escolar, 04510, Mexico DF, Ciudad Universitaria, Mexico

    Fidel Aroche Reyes

  2. Instituto de Investigaciones Economicas, Universidad Nacional Autónoma de México, Circuito Mario de la Cueva, 04510, Mexico City, Ciudad Universitaria, Mexico

    Marco Antonio Marquez Mendoza

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Correspondence to Marco Antonio Marquez Mendoza.

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Aroche Reyes, F., Marquez Mendoza, M.A. Demand-Driven and Supply-Sided Input–Output Models. J. Quant. Econ. 19, 251–267 (2021). https://doi.org/10.1007/s40953-020-00229-5

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