FOOTNOTES

*

 We should like to thank Martin Cerny for valuable criticism of the mathematical  apparatus and F. Nevaril, St. Kysilka and J. Mrenica who cooperated with us in the practical calculations.

1 V. D. Belkin, Tseny yedinnogo urovnya i ekonomicheskiye izmereniya na ikh osnove (Moscow. 1963); V. S. Nemchinov, ‘Osnovnye kontury modeli planovogo tsenoobrazovaniya., Voprosy ekonomiki, 12/1963; V. V. Novozhilov, Zakon stoimosti i planovoye tsenoobrazovaniye, (Leningrad, 1965); M. Korac, ‘Osnovni teorijski problemi analize ekonomskog polozaja privrednih grupacija’, Ekonomist (Beograd), 4, 1964; B. Csikos-Nagy, S. Ganczer, J. Rácz. ‘Az elsö termékrend szerü armodell’, Kozoazdasagi Szemle, 1/1964.  
2

  L. HejI, 0. Kyn, B. Sekerka, ‘Experimentalni propocty typu ceny’, Planovane hospodarstvi 11/1965.

3  Such a division is only roughly in accord with what is actually used: some elements of the first quadrant, or of the vector of social consumption and investment, are also priced in retail prices. The vector of personal consumption includes also consumption in kind. But these deviations are, from a practical point of view, unimportant and to keep our model as simple as possible we shall leave them out.
4 Column vectors will be represented by the symbol ’.
5   In this paper we shall always use the subscript 'diag' to designate a diagonal matrix.  
6

    This is in essence the so-called ‘inverse transformation problem’ of Morishima and Seton. (See M. Morishima, F. Seton, ‘Aggregation in Leontief Matrices and the Labour Theory of Value’, Econometrica, 1961.)

7 Oskar Lange, Teoria reprodukcji i akumulacji (Warsaw, 1961)
8  In case of subsidies some elements of the vector will be negative.
9 V. K. Dmitriyev, Ekonomicheskiye ocherki: (Moscow, 1904);
John von Neumann, ‘A Model of General Economic Equilibrium’, Review of Economic Studies, XIII (1945—46);
M. Morishima, F. Seton, ‘Aggregation in Leontief Matrices and the Labour Theory of Value’, Econometrica, 1961;
M. Morishima, Equilibrium Stability and Growth (Oxford, 1964);
P. Sraffa, Production of Commodities by Means of Commodities (Cambridge, 1963).
10 Costs in Czech: ‘náklady’ (N); Capital in Czech: 'fondy’ (F).
11

See G. Debreu and I. N. Herstein ‘Non-negative Square Matrices’, Etonometrica, vol. 21, 1953.

12

We want the new system to be of the single-level type, whereas the old system may be a double-level one, with a differentiated turnover tax rate.

13 Hejl, Kyn, Sekerka, ‘Experimentálni propocty typu ceny’, and ‘Vlastnosti dvoukanálove ceny’, Ekonomicky Casopis SAV, 6/1966.

 

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