Constant capital

Marx therefore develops a macroeconomic approach to establishing the conditions under which the economic system can reproduce itself one in which individual commodities are both produced and sold in the market place. To achieve this task, Marx collects industrial activities into two great departments of production. Department 1 produces means of production, capital goods that replace the constant capital (C,) used up in production. Department 2 produces consumption goods that take the form of variable capital (V ,) consumed by workers, and are also consumed by capitalists out of the surplus value (St) extracted from the production process. As a starting point for this analysis, Marx assumes that capitalists consume all of their surplus value. Hence, the system does not grow, since none of the surplus is set aside for capital expansion. All available resources are devoted to either consumption or the renewal of constant capital. This is the case of simple reproduction. 

Table 2.1 shows the first empirical example used by Marx (1978 473) to illustrate simple reproduction. Department 1 is assumed to produce nondurable outputs that are used up as constant capital during a single period... 

Marx also assumes the rate of surplus value (the ratio of St to VJ is the same in both departments. In Department 1, for example, 1,000 units of variable capital are employed at a rate of surplus value of 100 per cent, which generates 1,000 units of surplus value. Each worker performs an hour of labour for himself and an additional hour for the capitalist. The total amount of living labour performed (2,000) is added to the amount of constant capital (4,000) used up, to give a total value produced in Department 1 (W ) of 6,000. Similarly, Department 2 uses 2,000 units of constant capital, 500 units of variable capital, and extracts 500 emits of surplus value to yield a total value (W2) of 3,000. The general formula for calculating total values, Wt = Ct + IT +. S., is captured in Table 2.1. 

There are two main ways in which reproduction is made possible. First, the two departments have complementary requirements. Department 2 exchanges 2,000 units of its output of consumption goods for 2,000 emits of means of production produced by Department 1. These 2,000 emits of con-seimption goods fulfil the variable capital (1,000) and capitalist consumption (1,000) requirements of Department 1. And the 2,000 units of means of production supplied by Department 1 allow capitalists in Department 2 to replace used-up constant capital. Reproduction is facilitated by mutual exchange between the two departments. 

Second, the other 4,000 units of means of production, produced in Department 1, are required to replace used-up constant capital in Department 1. In Department 2, the 500 emits of variable capital and 500 units of surplus value are also produced and used up in Department 2 by its... 

Another of the great classical economists, Ricardo, is also charged with the same error, the contribution of the schema being to show how total social capital, with constant capital a constituent part, can be reproduced. 

The key difference is that Department 1 produces 6,000 units of capital goods, but only 5,500 are required to replace constant capital in the two departments.3 Department 2 now requires 1,500 units of capital goods in order to replace the amount it uses up. But Department 1 continues to produce a surplus of 2,000 units of capital goods (equivalent to 1,000 variable capital plus 1,000 surplus value) over and above the 4,000 it needs to replace constant capital. Therefore, the mutual exchange that took place between the two departments under simple reproduction, where surplus consumption goods were swapped for surplus capital goods, is only partially fulfilled. Marx (1978 587) explains that in each period of production the surplus of capital goods produced by Department 1 remains to be realized .4... 

Lianos (1979) provides an accessible insight into how the multiplier can be located in the reproduction schema. By focusing specifically upon Department 1 he states, it is convenient to assume a one sector economy (ibid. 407). Only information from Department 1 of the example used by Marx (Table 2.2) is included in the Lianos reproduction schema, as shown in Table 2.3. The key modification which enables a translation to Keynesian economic categories is to interpret all value added, variable capital plus surplus value, as net income (T,) for Department 1. Assuming away for the moment the problems associated with Adam Smith s dogma, this income is net of constant capital. The net income of the one-good economy is 2,000, consisting of 1,000 units of variable capital and 1,000 units of surplus value. 

An analytical leap can now be made that provides the cornerstone of the rest of this book. Located in this reproduction schema is a Keynesian multiplier that enables a relationship to be specified between net investment and net income. The intuition runs as follows. Capitalists anticipate that they will expand their constant capital by 500 in the next period of production. There is therefore a net investment demand for 500 emits of output to be produced in the current period.6 Workers are hired to produce this... 

This demonstrates that the scalar Keynesian multiplier relationship can in principle be derived from a two-sector model. As it stands, however, since (2.14) is defined using net income, no account is taken of the constituent role of constant capital in the production process.9 In embracing Keynes to model aggregate demand, a Marxian response is required to the charge that the scalar multiplier falls prey to Smith s dogma. 

To begin the analysis, Marx s numerical example of expanded reproduction can be recast as an input-output framework. Table 2.4(a) re-expresses the numerical elements of Table 2.2 as an input-output table. The advantage of this table is that it shows explicitly how Marx assumes capitalists spend their 1,750 units of surplus value on 500 units of new constant capital (dC), 150 new variable capital (clV) and 1,100 capitalist consumption (u). 

In this input-output format, elements of Table 2.4 can be read either along the rows as outputs of a particular department, or column-wise as inputs to that department. For example, reading row-wise, Department 2 produces 1,000 units of consumption goods for Department l s workers, 750 for itself, 150 for additional variable capital and 1,100 for capitalist consumption. Reading column-wise, Department 2 uses inputs of 1,500 constant capital from Department 1 and 750 of consumption goods from itself. The surplus value element of 750 is viewed as an input of value added to Department 2. For both departments, inputs and outputs are in balance, as shown by the identical column and row sums (6,000 and 3,000). 

The elements of Marx s numerical example are also represented in algebraic terms (Table 2.4b). Consider inputs of constant and variable capital to Department 2. The 1,500 units of constant capital are represented by P anXi, the money output of Department 1 required by Department 2. And the 750 units of variable capital are represented by p2h2l2X2, the amount of consumption goods set aside by Department 2 for its own use. 

The role of Marx s category of surplus value can therefore be identified in a macro scalar multiplier without the restrictive assumption of a one-good model. This scalar multiplier captures the inter-departmental structure of the reproduction schema without constant capital being assumed away. A formal model of aggregate demand in the reproduction schema is developed, which retains the simplicity of the Keynesian multiplier together with Marx s value categories. 

A first step in the analysis is to show explicitly how the elements of surplus value are allocated. Marx s numerical example of expanded reproduction (Table 2.2) can be explored in more detail by distinguishing, for each sector i, between capitalist consumption (uj, incremental changes in constant capital (cfQ and changes in variable capital (eft)). Numerical values for these terms are displayed in Table 3.1. In Department 1, for example, one half of the extracted surplus value of 1,000 is invested in the expansion of capital, with 400 directed to new constant capital and 100 to new variable capital. The remaining 500 units of surplus value are consumed by Department 1 capitalists. 

It should also be emphasized that this adaptation of the Kalecki system represents an interpretation of the reproduction schema that is consistent with Marx s system. As Lee (1998) has argued, Kalecki has a restrictive production model in which each department is vertically integrated, producing its own raw materials. In contrast, Marx assumes that raw materials are a part of constant capital, produced in the first department and circulated to other departments. A failure to fully take into account connections between industries leaves the Kalecki system vulnerable to a SrafFian critique. Steedman (1992), for example, has lambasted the Kaleckian price system for the absence of multisectoral relationships. By establishing the Kalecki principle in an input-output context, an interpretation of the reproduction schema is possible in which linkages between industries are taken seriously. 

It should be noted that this model also provides a modification of the standard Marxian representation of the circulation of money, since only wages are advanced. In the standard interpretation of Marx s system, the total amount of money (M) that firms advance consists of variable and constant capital, which is transformed in the production process to a new volume of money (M ) that includes profits made by firms. However, for Graziani ... 

The workers use this 1,000 to purchase means of consumption of the same value from the capitalists in department II, and thereby transform half of department II s constant capital into money. The capitalists in department II, for their part, use this 1,000 to buy means of production to the value of 1,000 from the capitalists in department I. 

Following the approach worked out in Chapter 3, Table 4.1 shows that in the Kalecki-type formulation profits in each sector are defined in gross terms, consisting of expenditure on the replacement of existing constant capital and its expansion (C, + e/C.) whereas in Table 4.2 profits (/() are defined in net terms (dC, + dV,). The latter definition of profits is consistent with Marx s interpretation, with the total increment of capital identical to the volume of surplus value, after accounting for the replacement of current inputs of constant and variable capital. 

The role of inventories in the reproduction schema can be illustrated using Marx s numerical example (Table 4.3a). The elements of this schema can be recast in a tableau representing three periods of production, as shown in Table 4.4. Outputs of the production process are represented for this year and last year. First, the outputs of last year are shown as inputs of production in the current period. For example, the 4,000 units of constant capital used up by Department 1 this year were produced by Department 1 in the previous year. Similarly, the 1,000 units of variable capital (consumption goods) used up by Department 1 this year were produced by Department 2 in the previous year. 

Department 1 produces 4,400 capital goods this year that are used up next year. This sum includes (1) 4,000 units that are required to replace the 4,000 units used up this year and (2) 400 additional units of constant capital that are used to expand production in the next period. Similarly, Department 2 produces 800 units of consumption goods that are used in the next period, 50 of which represent an expansion of variable capital in Department 2. For simplicity, it can be assumed that capitalist consumption goods are produced and consumed in the current period of production. 

The starting point for the circulation of money, under the auspices of the Kalecki principle, is the expenditure outlays of the capitalist class. In Table 4.5, the composition of these expenditures is made up of money outlays on capitalist consumption ( ) and new constant and variable capital (dC and dV). Outlays are made by capitalists in each department of production. For example, the capitalists in Department 1 spend 400 units on new constant capital, 100 units on new variable capital and 500 units on capitalist consumption. The outlays on the products of both departments are collected in the final row as total outlays, which sum to 1,750. Depending upon what is purchased, each outlay is also a receipt. Department 1 s purchase of 100 consumer goods from Department 2, for example, is a receipt for Department 2. The final column of Table 4.5 collects these receipts, which make up 1,750. The capitalist class outlays 1,750 in total, which returns to it as 1,750 in receipts. 

Second, the scalar term representing money constant capital can be re-expressed as... 

However, under expanded reproduction a much more demanding requirement is placed on the circuit of money. Capitalists increase then-capital outlay on new elements of constant and variable capital. If we define dC as new constant capital and dV as new variable capital, there is an extra amount of money (dC + dV) that is required to service expanded... 

Table 5.1 shows the two-department expanded reproduction schema over five years.2 The familiar assumption of a constant rate of surplus value of 100 per cent is maintained, together with a 4 1 ratio of constant to variable capital in Department 1 and a 2 1 ratio in Department 2. Constant capital inputs are non-durable, used up dining a single period of production, and 1 of output is assumed equal to a unit of labour. 

Key to this economy s capacity to expand is the production of sufficient surplus value to invest in additional units of capital. Marx assumes that a half of surplus value in Department 1 is invested in this way. For year 1 this means that 500 of the total 1,000 units of surplus value produced in Department 1 are directed to 400 units of new constant capital and 100 units of new variable capital. In year 2 constant capital expands from 4,000 to 4,400 units, and variable capital from 1,000 to 1,100 units, maintaining the 4 1 ratio between constant and variable capital. A new position of balance is established by also maintaining Department 2 at its original 2 1 ratio. 

Year Constant capital Variable capital Profits Net income dy/y / dl/I... 

This introduction to simple reproduction, from an input-output perspective, paves the way for a consideration of the more relevant and complex case of expanded reproduction. Table 6.3(a) is the numerical input-output representation of the expanded reproduction schema (see Table 2.4). In algebraic terms, the expansion of constant capital is represented by dC and new variable capital by dV. Table 6.3(b) shows the set of input-output accounts using Marxian notation, with the new role for capital accumulation represented alongside the terms previously modelled under simple reproduction. 

Comparing this to the condition for simple reproduction (6.1), the only difference is the element for expansion of constant capital dC. This illustrates Marx s claim that the condition of simple reproduction lives on as a structural entity under expanded reproduction. It also follows that the proportionality condition for expanded reproduction is implicitly assumed in the input-output accounts. 

The exchange of commodities between producers is underpinned by Marx s theory of value. In contrast to Adam Smith, a correct distinction is made by Marx between dead and living labour (see Chapter 2). Constant capital - raw materials, machinery and premises - are produced by past labour, in previous periods of production. Variable capital and surplus value are produced by living labour in the current period of production. For Luxemburg ... 

The fatal error committed by Smith is to ignore the role of constant capital a mistake that is attributed to his undeveloped theory of value. 

For each individual capitalist, therefore, the value of each commodity is made up of constant capital, variable capital and surplus value. Moreover, commodities have value in exchange only when they are sold in their money form. Once the commodity has been produced, it must be realized, it must be converted into a form of pure value that is, into money (ibid. 38). However, when Luxemburg examines the reproduction of total capital, the use-form of commodities is also important. 

Key to the Bauer model is an assumption that constant capital increases at a higher rate than variable capital - the former increases at 10 per cent per annum and the latter at 5 per cent (ibid. 67). The result is a continual increase in the organic composition of capital, the ratio of constant to variable capital. The rate of surplus value, the ratio of total surplus value to variable capital, is assumed to remain constant at all times. With variable capital increasing at 5 per cent each year, the same increase in the pool of total surplus value takes place, out of which additional increments of constant and variable capital are funded. Capitalist consumption is treated... 

At the outset the economy employs 200,000 units of constant capital and... 

Year 2 shows a new input of 220,000 units of constant capital incorporating the additional 20,000 units produced in the previous period and a new 105,000 units of variable capital incorporating the additional 5,000 units of variable capital. With the rate of surplus value remaining the same, a new pool of 105,000 units of surplus value is produced, and disposed of with further increases in constant capital (by 22,000) and variable capital (by 5,250). The residual volume of capitalist consumption, after funding the capital expansion, is 77,750. Note that although there is an increase in capitalist consumption, the proportion of profits consumed by capitalists falls to 74.05 per cent compared to 75.00 per cent in year 1. 

This reduction in the proportion of profits consumed has important consequences for the economy as the simulation is repeated over subsequent periods. Although Bauer was able to demonstrate that expanded reproduction is sustainable over a four-year period Grossmann showed that if the simulation is continued for 35 years then this results in economic breakdown. Table 7.1 shows a steady fall in the proportion of profits consumed until, in year 34, only 2.16 per cent are consumed. The stringent demands of capital accumulation are fulfilled with constant and variable capital increasing by 10 and 5 per cent respectively throughout the 35-year period. The problem, however, is that with variable capital failing to keep pace with constant capital the pool of surplus value extracted from variable capital also fails to keep pace. 

The portion of surplus value destined for accumulation as additional constant capital... increases so rapidly that it devours a progressively larger share of surplus value. It devours the portion reserved for... 

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