Abstract
This introductory chapter outlines the central relationships amongst classical, traditional neoclassical and modern classical theories of value, distribution and capital. It then argues that the state variable representation of linear systems could be conceived of as an approach for revealing the essential properties of a linear system of production of commodities and positive profits by means of commodities and, therefore, determining the extent to which these properties deviate from those predicted by the traditional capital theories.
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As Kurz (2014, p. 11) remarks, ‘the same kind of criticism can be found also in most recent times’ (and refers, as an example, two papers by Kenneth J. Arrow, published in 1972 and 1991).
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See Bhaduri (1966), Pasinetti (1966), Garegnani (1970), Steedman (1979a, b), Kurz and Salvadori (1995) and the references therein. In modern classical economics system, the real wage rate(s) is not necessarily an exogenously given variable. That system determines relations between, on the one hand, distributive variables and commodity prices and, on the other hand, growth , physical outputs and labour allocations. Thus, there are alternative ways of closing it (consider, for instance, the ‘monetary theory of distribution ’, i.e. the possible determination of the profit rate by the money interest rate ; Sraffa 1960, p. 33, Panico 1988, Pivetti 1991).
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Matrices (and vectors) are delineated in boldface letters. The transpose of a 1×n vector ψ ≡ [ψ j] is denoted by ψ T. The diagonal matrix formed from the elements of ψ will be denoted by \( \widehat{\boldsymbol{\uppsi}} \), and I will denote the n×n identity matrix.
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By definition, this axiomatization is incomplete for systems that include agents’ expectations about the future. In that case, ‘the future influences the present just as much as the past’ (Friedrich Nietzsche) and, therefore, the concept of futurität (futurity ) becomes indispensable (see, e.g. Willke 1993, Chap. 4).
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If there is not a complete set of eigenvectors, matrix A cannot be reduced to a diagonal form by a similarity transformation and, therefore, the original system cannot be decomposed into a set of uncoupled first-order sub-systems (we will return to this issue in Chap. 2). It is always possible, however, to find a basis in which A is almost diagonal (‘Jordan normal form ’; see, e.g. Meyer 2001, Sects. 7.8 and 7.9). In that case, the transformed system (also) contains ‘chains’ of first-order sub-systems (associated with a particular system eigenvalue), where the output of one is the input of another.
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In that case, the eigenvalues of [A–I] all have negative real part (and vice versa); thus, the equilibrium point of system (1.1a), with γ(t)=γ, is asymptotically stable.
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Mariolis, T., Tsoulfidis, L. (2016). Old and Modern Classical Economics. In: Modern Classical Economics and Reality. Evolutionary Economics and Social Complexity Science, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55004-4_1
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