# 〔当代经济研究1701〕弗里曼-克莱曼问题探索：基于里昂惕夫投入产出模型的分析

1.实物生产模型

a_{ij}=\frac{x_{ij}}{x_j}

（2）

（3）

（4）

（5）

（6）

（二）价值生产模型

（7）

（8）

（三）扩大再生产

（9）

（10）

（11）

（12）

####三、一个简单实例的说明

（一）简单再生产

（二）外延式扩大再生产

（三）内涵式扩大再生产（马克思有偏技术进步）

1-2 农业 制造业 消费+积累 总产出

（四）相关指标的变动趋势

（技术不变） 扩大再生产
（有偏技术）

（以初始价格计） 320 450 641 675

（以当期价格计） 320 450 620 711.75

####四、研究结论

[1] Duménil G, Lévy D. A Stochastic Model of Technical Change: an Application to the US Economy(1869-1989)[J].Metroeconomica, 1995(3):213-245.
[2] Foley D, Michl T. Growth and Distribution, Cambridge: Harvard University Press, 1999.
[3] Shaikh A. Wages, Unemployment and Social Structure: A New Phillips Curve[R]. Department of Economics, New School for Social Research. Working Paper, 2013.
[4]李海明.一个古典-马克思经济增长模型的中国经验[J].北京：经济研究，2014（11）：159-169.
[5]斯拉法.用商品生产商品—经济理论批判绪论[M].巫宝三译.北京：商务印书馆，1991.
[6]瓦西里·里昂惕夫.投入产出经济学[M].崔书香译.北京：商务印书馆，1982.
[7] Morishima. Marx’s economics-A dual theory of value and growth [M]. Cambridge : Cambridge University Press, 1973.
[8] Freeman A, Kliman A.Two concept of value, two rates of Profit, two laws of motion[J].Value, Capitalist Dynamics and Money,2000
(18):243-267.
[9]吴易风.马克思主义经济学与西方经济学比较研究（第3卷）[M],北京：中国人民大学出版社，2014.
[10] Adalmir, Marquetti . Analyzing historical and regional patterns of technical change from a classical-Marxian Perspective[J].Journal of Economic Behavior & Organization, 2003 (2):191-200.

An Analysis on the Problem of Freeman & Kliman—Based on the Leontief Input-Output Model
Li Mengfan, Xie Lu, Han Wenlong
Abstract Measuring profit rate from three dimensions, which are physical, price and value would result in differences, and this theoretical proposition can be called the Problem of Freeman & Kliman. With Leontief input-output model, this paper builds up a Marxist analysis framework on the change process of the price and value, in order to verify the problem of Freeman & Kliman. By introducing “Marx biased technological progress” in the model, this paper found that with the technological progress, organic composition of capital would increase, and at the same time the surplus value rate would also increase. In addition, in the connotative expanded reproduction process, technology progress would affect physical proportion of productive input factors, which would in turn change the productive coefficient matrix, affect price of products and the distribution relationship between capitalists and workers.
Key words Marx biased technological progress; Input-output analysis; Economic growth