Welcome to LI Bangxi's Website

Name:    LI Bangxi

Affiliation: Professor Dr. FUJIMORI Yoriaki Lab.

       Graduate School of Economics

       WASEDA University

       Tokyo 169-8050, Japan

Email:    libangxi[at]gmail.com

❖ Li, Bangxi and Yoriaki Fujimori (2011b), "Marx-Sraffa Equilibria and Eigenvalue Problems: A Moore-Penrose Pseudoinverse Approach", Political Economy Quarterly (Japan Society of Political Economy), Vol.48, No.3, pp.56-68.[In Japanese, PDF,373KB]

In this paper, we inherited Hua LooKeng’s problem consciousness, and we investigate the stability of price equilibria of Marx-Sraffa joint-production system, where equilibrium is defined in terms of equalities with rectangular matrices, from the angle of eigensystems. We transform the problem of searching equilibiria of Marx-Sraffa joint-production systems into eigenvalue problems by means of Moore-Penrose inverses.
 First, we give an overview of Sraffa-Okishio-Nakatani (SON) reduction from the angle of nonsingular transformation. SON dealt with a limitted joint production system in which only aged fixed capital is produced jointly. In SON, elimination of terms related to aged fixed capital leads to the determination of profit rates and prices of brandnew commodities. It is shown that this elimination in SON gives a decompostion of coefficient matrix into three parts; the first one concerns only brandnew commodities, the second aged fixed capital to brandnew fixed capital, and the third part zeros.
 Second, it is shown that the second part of the above decomposition is exactly the companion matrices in renewal dynamics of fixed capital discussed by Yamada-Yamada.
 Thirdly, by assuming the rank condition on input and output matrices, we demonstrate that price equilibria of general joint production system of the Marx-Sraffa style can be transformed into an equivalent eigenvalue problem by means of MP-inverses.
 We give a numerical example after the theory.
 Since the resulting square matrices of the eigensystem are no longer necessarily nonnegative, the dominant eigenvalue is not the one corresponding to equilibria. In this sense, one cannot assert that price equilibrium is stable. In SON, price equilibrium is dynamically stable, because the relative prices of aged fixed capital are determined separated from the determination of profit rates. The rate of depreciation which depends on profit rates is applied therein. In this sense, the accounting system of amortisation is an stabilizing effect in the economy.

❖ Li, Bangxi (2011a), "Economic Durability of Fixed Capital", Waseda Journal of Political Science and Economics, No.381-382, pp.17-25.[In English, PDF,151KB]

This paper discusses the determination of economic durability of fixed capital in the case in which efficiency of fixed capital decreases as it is used. The framework of analysis is a linear multisector model a la Marx-Sraffa. A numerical simulation is the basic tool. Main results are: (i) the economic duralibity of fixed capital is dependent on the profit rate; (ii) the economic durability of fixed capital tends to increase as the profit rate increases.

❖ Fujimori, Yoriaki and Bangxi Li (2010b), "Replacement of Fixed Capital as a Markov Process", China Review of Political Economy, Vol.1, No.4, pp.116-27.[In Chinese, PDF,195KB]

This paper shed light on the Yamada-Yamada model of dynamics of fixed capital from the angle of the Markov process. The original Yamada-Yamada model is a higher order difference equation with respect to the quantity of nominal fixed capital. In that model, the so-called Ruchti-Lohmann effect is taken into account. Yamada-Yamada shows, by means of Kakeya's theorem, that the oscillations accompanying the Ruchti-Lomann effect is damping.
 We investigate the characteristic polynomial of their difference equation. The least polynomial of the characteristic polynomial of the Yamada-Yamada model has a companion matrix which represents a Markov process. This paper shows that the left Perron-Frobenius vector of the companion matrix gives the proportions of prices of aged fixed capital, while the right one gives the equilibirum quanities of aged fixed capital of the steady state.

❖ Li, Bangxi and Yoriaki Fujimori (2010a), "Fixed Capital and Cambridge Equation", Economic Theory and Business Management (Renmin University of China), No.7, pp.24-9.[In Chinese, PDF,201KB]

This paper shows two points. In a Marx-Sraffa system, in which aged fixed capital is dealt with as a joint-product, the Cambridge equation holds true. If the Marx-Sraffa system is simplified to the extended Leontief system, in which aged fixed capital is excluded à la Okishio-Nakatani, the Cambridge equation does not hold.

❖ Li, Bangxi (2009), "Fixed Capital and Standard Commodity", Economic Theory and Business Management (Renmin University of China), No.3, pp.26-31.[In Chinese, PDF,176KB]

This paper discusses the extension of Sraffa's standard commodity to the case in which fixed capital is explicitly considered.
 In a von Neumann framework where second-hand fixed capital is considered, a generalised standard operation vector can be defined, so that trade off between wages and profits in terms of the generalised standard operation vector is expressed by a line.
 If second-hand fixed capital is eliminated and only brandnew fixed capital is considered, no linear trade off between wages and profits can be observed, even if trade off between them is measured in terms of a generalised standard commodity.

❖ Li, Bangxi (2008), "China Input-Output Table and Linear Economic Theory", Political Economy Quarterly (Japan Society of Political Economy), Vol.45, No.2, pp.66-71.[In Japanese]

In this paper, some important quantitative concepts of linear economic theory were calculated by using the China 1987-2002 input-output tables.
 First, the wage-profit curves were drawn and the relative positions of actual economic state were estimated. Second, Marxian 2-sector tables were constructed from input-output tables, and some important parameters such as organic composition of capital, rates of surplus value, rates of profits were estimated. Third, the turnpike path of the China economy was calculated by arranging 2-sector coefficient matrices in order from 1987 till 2002. It is seen that the actual growth path from 1992 till 2002 runs close to this turnpike path.

❖ Li, Bangxi (2011), "Estimation of Marginal Fixed Capital Coefficient and Wage-Profit Curves a la von Neumann-Leontief: A Case Study of China's Economy 1987-2000", Waseda Economics Working Paper Series (Graduate School of Economics, Waseda University) No.11-001. [In English, Downloadable, 120KB]