Abstract
We examine the Pasinettian multi-sectoral two-class model with a microfoundation of a capitalist and a worker. The microfoundation assumed in this study is an infinitely lived agent and an agent whose behaviour follows the overlapping generations model. We consider two combinations of the microfoundation of capitalists and workers: one is that both capitalists and workers act as infinitely lived agents and the other is that capitalists act as infinitely lived agents and workers act as in the overlapping generations model. We exclusively analyse the steady states and focus on the switches of equilibria from the Pasinetti equilibrium to the dual equilibrium and vice versa, together with the paradoxes in capital theory. The relationship between the rates of economic growth and profit obtained in Pasinetti equilibrium is independent of technology and the combination of the microfoundation. The relationship obtained in dual equilibrium is dependent on technology and differs, depending on the combination of microfoundation. A numerical example shows the simultaneous analysis of the switch of equilibria, income distribution, and capital theory paradoxes. The result indicates that it is necessary to reconsider the importance of capital as a bundle of reproducible and heterogeneous commodities to construct an alternative model analysing the distribution of income and capital (wealth), which is unaccountable by the standard neo-classical models with capital as the primary factor of production.
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Notes
See also Pasinetti (1964, 1966a, 1966b, 1974). Baranzini and Mirante (2018: Chaps. 6, 7) provide an excellent survey of the extensions of the Pasinettian two-class model. Baranzini and Mirante (2018: pp. 86–89, pp. 212–214) show us the correspondence among Hahn, Kaldor, and Pasinetti with respect to Pasinetti (1962).
Baranzini (1991) is an early example of the models introducing the OLG into the Pasinettian two-class model.
Mattauch et al. (2016) investigate the distribution of wealth in relation to public investment in a model with high-income households that are ILA and middle-income households that follow the OLG model. Their analysis focuses on the equilibrium at which both types of households survive in the steady state (i.e. PE).
In contrast to Kaldor’s (1961) old stylised facts, the new ones proposed by Stiglitz (2016) are:
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There is growing inequality in both wages and capital income (wealth), and growing inequality overall;
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Wealth is more unequally distributed than wages;
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Average wages have stagnated, even as productivity has increased, so the share of capital has increased;
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The wealth ratio has increased significantly;
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The return on capital has not declined, even as the wealth–income ratio has increased.
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Stiglitz (2016: pp. 15–16) mentions the possibility of such phenomena arising, yet assumes a perfectly neo-classical technology in his model.
Here, we do not consider technical progress in that the row or the column of \({\varvec{A}}\) and \({\varvec{L}}\) changes as time goes by. In other words, m and n are fixed over time.
Although it is assumed that both the capitalist and worker control \({\varvec{q}}_{t+1}\), we do not need to apply the differential game to our problem. This is because the non-substitution theorem holds in the economies assumed in this study. According to the theorem, any \({\varvec{q}}_{t+1}\ge {\varvec{0}}\) is efficient and, as we show in Subsect. 3.1.4, the solution of the capitalist’s problem is consistent with that of the worker’s problem in an economic system. Regarding the application of the differential game to the Pasinettian two-class model, see Chappell and Latham (1983).
The numerical example is from Vienneau (2005).
Given that the profit share is obtained by the rate of profit multiplied by the capital coefficient, the extent of the decline in the capital coefficient is great enough to offset the rise in the rate of profit around the switch point. Therefore, the profit share also declines.
According to Burmeister (1980: p131), this peculiar assumption is that the so-called real Wicksell effect is negative for all feasible \(r>0\):
$$\begin{aligned} {\displaystyle \sum \limits _{i=1}^{n}} p_{i}\left( r\right) \frac{\text {d}k_{i}\left( r\right) }{\text {d}r}<0, \end{aligned}$$where \(p_{i}\left( r\right)\) and \(k_{i}\left( r\right)\) denote the relative price of commodity i and the per capita amount of the commodity necessary as the capital input, respectively. As our analysis shows, it is not necessary to assume that the inequality is likely to be satisfied.
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An earlier version of this paper was presented at the International Conference on Economic Theory and Policy, held on 16–18 September 2018 at Meiji University in Japan; the 9th Summer School on Analytical Political Economy, held on 26–28 August 2019 at Doshisya University in Japan; and the 10th Annual Conference of the Keynes Society Japan, held on 5–6 December 2020, by using Zoom. The author is grateful for helpful comments and suggestions from the participants, especially Toichiro Asada, Hiroyuki Ozaki, Neri Salvadori, Hiroaki Sasaki, and Naoki Yoshihara. In addition, the author gives special thanks to the two anonymous referees for their helpful comments and suggestions, which substantially improved this paper. He is solely responsible for all remaining errors. Finally, financial support from the Japan Society for the Promotion of Science KAKENHI (Grant Number JP17K03615) is gratefully acknowledged.
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Kurose, K. A two-class economy from the multi-sectoral perspective: the controversy between Pasinetti and Meade–Hahn–Samuelson–Modigliani revisited. Evolut Inst Econ Rev 19, 239–270 (2022). https://doi.org/10.1007/s40844-021-00202-8
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DOI: https://doi.org/10.1007/s40844-021-00202-8