Before we start dealing with the proper subject of this paper, we shall modify somewhat the Marxian division of economy into departments, in order to simplify our argument and to focus on the basic problem of the reproduction schemes.
First, instead of including producer goods in Department 1, we will assume that it covers the total value of gross investment inclusive of the respective raw materials. Thus this department represents the integrated production of all final non-consumer products. (We disregard in our argument, as does Marx--when he deals with reproduction schemes--both foreign trade and government revenue and expenditure.)
Second, we treat likewise the consumer goods, i.e. we include in the department which covers their output the production of respective raw materials from top to bottom. Moreover, fully in the Marxian spirit, we distinguish the following two departments: Department 2, producing consumer goods for capitalists, and Department 3, producing wage goods.
We obtain thus the following tableau économique of the national income, where P1, P2, P3 are gross profits (before deduction of depreciation) in the respective departments; W1, W2, W3 are the respective wages; P and W are aggregate profits and wages; and finally I is gross investment, Ck capitalist consumption, Cw worker consumption, and Y gross national income (before deduction of depreciation).