Document Type


Date of Award



Marxian economics, Mathematical models

Degree Name

Doctor of Philosophy (PhD)



First Advisor

Melvin Leiman

Second Advisor

Jung Chao Liu

Third Advisor

Jan M. Michal


In the first two volumes of Capital it is assumed that commodities are exchanged according to their values; with different organic compositions of capital for each sector of the economy this assumption leads to different rates of profit, a result which is not consistent neither with the reality of a capitalist system nor with the Marxian assumptions. Marx points out the problem in the third volume of Capital where he introduces the concept of prices of production (cost plus average profit on capital employed) as deviations from the actual values of the commodities. He maintains that when the economy enters the capitalist stage, the rate of profit cannot be unequal among the different sectors; even if unequal profit rates exist at some particular period of time, competition among capitalists creates the mechanism for profit rate equalization. As a result, prices at which commodities are exchanged do not strictly correspond to the quantity of labor expended in their production. He concludes that the law of value operates directly in the first case and indirectly in the second modified into prices of production.