A brief biography of Marx and a summary of his key works in political economy

Karl Marx was born in 1818 in Trier, then in the Prussian Rhineland, now in Germany close to the border with Luxembourg. He studied law and philosophy at Bonn and Berlin, taking out his doctorate in 1841. He then moved to Cologne where he worked as a (radical) journalist and newspaper editor. Difficulties with the censors led to the suppression of the newspaper in late 1843 at which time Marx moved to Paris. It was in Paris that he embarked upon his quest to develop a ‘scientific socialism’ and began a serious (and what would turn out to be a lifelong) study of political economy. In early 1845, he was forced to leave France and moved to Brussels. In Brussels (and, to a lesser extent, earlier in Paris), he was actively involved with German emigres and other socialists and communists and it was in Brussels that he wrote (together with Engels^{Footnote 1}) the Manifesto of the Communist Party. In March 1848, Marx was expelled from Brussels and moved to Cologne. In June 1849, he returned to Paris following an order to leave Prussia. Expelled from Paris in August 1849, he moved to London where he resumed his study of political economy and further refined his own ideas. Apart from brief visits to the continent, he spent the rest of his life (in other words, the major part of his adult life) in London. During this period, he wrote and published a great deal. He was also very active in worker’s associations and especially the International Workingmen’s Association (aka the First International) founded in 1864. He died in London in 1883 and is buried in Highgate Cemetery.

From the point of view of political economy, his most important works include Economic and Philosophic Manuscripts of 1844 (aka The Paris Manuscripts, written in 1844 but first published in 1932); A Contribution to the Critique of Political Economy (first published in 1859); a pamphlet Wages, Price and Profit (aka Value, Price and Profit, written in 1865 and first published in 1898); Capital Volumes 1–3 (first published in 1867, 1885 and 1894, respectively); and Theories of Surplus Value (aka Capital Volume 4 – this is actually made up of three related volumes, first published in 1905–1910). A brief note on each of these works follows.

The concept of an economic surplus

The key idea is that economic and social progress (and, in particular, the accumulation of capital) entails the employment of some workers to do things other than to produce the food and other ‘necessaries’ which make up the basket of goods and services which workers consume. However, for this to happen, the workers who produce the goods and services that workers consume (wage-goods) must produce more than they (the workers producing wage-goods) themselves consume. In other words, the workers in the wage-goods sector must produce ‘a surplus’ of wage-goods.

In what follows, I will call the excess of the output of wage-goods over the consumption of wage-goods by the workers in that sector, ‘the economic surplus’. Two obvious questions are as follows: (1) what determines the size of the surplus, and (2) what might it be used for? We shall leave the second question until later, when we shall see that Marx’s views on this are far more nuanced than many people think. We begin with the determination of the size of the surplus.

Since production is a ‘flow’ concept, we must begin by deciding the length of the time period we will use as the basis for our measures. Since it will link up with a very important element of Marx’s ideas, I will, for the moment, measure things on a daily basis.

Measured in units of output, the surplus will be the difference between the (average) amount a worker in the wage-goods sector produces in a day (I will use A_wg as the symbol for this) and the worker’s (average) daily consumption of wage-goods. Under the assumption that workers consume all their income and do not save, their daily consumption will equal their real wage per day (w_r). This means that each worker will, on average, be producing a surplus of $(A_{wg}-w_r)$ units of output each day and so the total surplus produced by all workers in the wage-goods sector each day will be L_wg (A_wg − W_r), where L_wg is the number of workers in the wage-goods sector.

Thus far, we have measured the economic surplus in units of output, but it is possible to measure it in units of labour or ‘labour time’. Let us go back to a single worker who is producing a surplus of $(A_{wg}-w_r)$ each day. If we divide this by the real wage, we will have a measure of the size of the surplus in units of labour, that is, a measure of the number of workers outside the wage-goods sector that the surplus originating in the wage-goods sector can sustain. A measure of the surplus in units of labour for a single worker employed in the wage-goods sector will be

(1) $\frac{\left(A_{wg}-w_r\right)}{w_r}=\frac{A_{wg}}{w_r}-1$

In the next two sections of the article, we will see that the surplus is related to ‘unpaid labour’ and ‘exploitation’.

Paid and unpaid labour time

In this section, I shall again confine myself to looking at that sector (that combination of industries) which produces wage-goods – the goods and services which workers consume. I shall assume that the sector is vertically integrated, and thus we can think of it producing its own raw materials.

Following Marx’s lead, let us look at work taking place over a typical day. Let

We know that real profits per worker per day in the wage-goods sector (π_wg) will be the difference between real output per worker over the whole of the working day and the real daily wage. This is

${\pi }_{wg}=\left(a_{wg}\times h\right)-w_r$

Notice that we can rewrite this as

${\pi }_{wg}=a_{wg}\left(h-\frac{w_r}{a_{wg}}\right)$

Since a_wg is the amount a worker can produce in 1 hour, the ratio $w_r/a_{wg}$ must be the number of hours a worker in the wage-goods sector would need to work to create a volume of output equal in value to the (daily) real wage. Marx refers to this number of hours as ‘paid labour’ or ‘necessary labour hours’; I shall use the symbol $h^{*}$ for this.

Since $h^{*}=(w_r/a_{wg})$ , we can write the expression given above for (real) profits per worker in the wage-goods sector in terms of the gap between h and $h^{*}$

(2) ${\pi }_{wg}=a_{wg}\left(h-h^{*}\right)$

Hence, Marx’s (uncontroversial, I’d have thought) view that profits must be a reflection of ‘unpaid labour time’ or ‘surplus labour’. He writes,

Unpaid labour and exploitation

An important element in Marx’s view of history is the idea that by one means or another in the prehistory of capitalism, the mass of the people are dispossessed of any ‘means of production’ they own or have free access to, including land, raw materials and (especially) capital goods. He explains how it came about that means of production get to be privately owned by ‘a few’, and thus how the capitalists can find workers on the labour market ready and willing to work for them, in the last part of Capital Volume 1 (Chapters 26–33). Among the examples he gives of this process (he refers to it as ‘primitive accumulation’) are the clearances and enclosures in Scotland and England. He also mentions Australia in this context (in Chapter 33) – indeed, he argues that the Australian colonial experience reveals the true nature of capitalism, namely, that ‘capital is not a thing, but a social relation between persons’. This is explained with reference to Wakefield’s theory of colonisation:

Elsewhere, he writes,

It is the idea (fact?) that workers in a capitalist economy have no option but to work for others (because they do not own or control the ‘means of production’, including land) that leads Marx to describe unpaid labour or surplus labour as ‘exploitation’. To him, this is an essential part of the nature of capitalism because ‘Capital … is essentially the command over unpaid labour’ (Reference MarxMarx, 1954: 500).

But, it is important to note that Marx explicitly rejects the ‘moral’ aspect of exploitation and restricts the concept to a ‘factual’ and ‘scientific’ description of labour relations under capitalism.

In his Marginal Notes on Adolph Wagner, Reference Marx, Engels and MarxMarx (1989) writes,

He goes on to say,

Engels summed up the matter in his preface to the first German edition of Reference Marx and EngelsMarx’s (1963) work The Poverty of Philosophy:

Time and again, Marx says that ‘the equitable criterion of “exchange of equals” was honoured in the capitalist system’ (Reference RoncagliaRoncaglia, 2005: 255). Reference MarxMarx (1954) writes, for example, that

Elsewhere, he writes,

But this ‘equality’ does not extend to the production process itself. There we see unpaid labour time, masked by the appearance that workers are paid for all of their labour time. Marx thus stresses the difference between nominal, money or ‘apparent’ magnitudes and real magnitudes. In this context, he repeatedly points out that in a ‘wages system’, all hours of work appear to be paid (after all workers receive payment in the form of money for every hour they work). He writes, for example, ‘On the basis of the wages system even the unpaid labour seems to be paid labour’ (Reference MarxMarx, 1947: 37). The amount of money

We turn now to look at the relationship between unpaid labour and the functional distribution of income.

The (functional) distribution of income

Given equation (2) and given also our definition of $h^{*}$ , it must be the case that the ratio of profits to wages in the wage-goods sector will be

(3) $\frac{{\pi }_{wg}}{w_r}=\frac{{\pi }_{wg}/a_{wg}}{w_r/a_{wg}}=\frac{h-h^{*}}{h^{*}}=\frac{h}{h^{*}}-1$

We can use this expression as the foundation for a first look at one of the key concepts in Capital, namely, ‘the rate of surplus value’ or ‘rate of exploitation’. Reference MarxMarx (1954) writes, ‘Capital … compels the working-class to do more work than the narrow round of its own life-wants prescribes’ (p. 293) and ‘the rate of surplus-value is … an exact expression for the degree of exploitation of labour-power by capital, or of the labourer by the capitalist’ (p. 209). Elsewhere, he writes,

Notice that there is an intimate connection between the size of the economic surplus discussed above and the rate of surplus value. We can see this by comparing equation (1) with equation (3). Taken together, they imply that

(4) $\frac{\left(A_{wg}-w_r\right)}{w_r}=\frac{A_{wg}}{w_r}-1=\frac{a_{wg}h}{a_{wg}{h}^{*}}-1=\frac{h}{h^{*}}-1=\frac{h-h^{*}}{h^{*}}=\frac{{\pi }_{wg}}{w_r}$

Among other things, this tells us that there is a one-to-one mapping between the size of the economic surplus, the extent of any unpaid labour and (the functional) income distribution.

It is easy to show that the ratio of profits to wages (see equation (4)) and the rate of surplus value are related to the ‘wage share’ – that is, the ratio of the real wage per worker to real output per worker (in the wage-goods sector):^{Footnote 5}

The wage share (S_wg) will equal

$S_{wg}=\frac{w_r}{A_{wg}}=\frac{w_r}{a_{wg}\times h}$

Since the ratio $w_r/a_{wg}$ is the number of hours a worker in the wage-goods sector would need to work to create a volume of output equal in value to the real wage – that is, $h^{*}$ – we can write our expression for the wage share as

(5) $S_{wg}=\frac{w_r}{A_{wg}}=\frac{h^{*}}{h}$

For future reference, note that a fall in the wage share will be associated with a fall in $h^{*}/h$ and thus a rise in the ratio of unpaid to paid labour, that is, a rise in the rate of exploitation (see equation (3)). This means that those things which determine the behaviour of the wage share over time are also determining the behaviour of the rate of exploitation (and vice versa).

Of particular interest to Marx (and the other classical economists) is understanding the relationships between the size of the economic surplus of wage-goods, the rate of capital accumulation in an economy and the wage share in the wage-goods sector – and thus the ratio between paid and total about hours and the rate of exploitation. We will look at this in the next section of the article.

The real wage, the wage share and capital accumulation

Again, following Marx, let there be two sectors, one sector produces wage-goods – the goods and services which workers consume (it will continue to be denoted by the subscript ‘wg’) – while the other sector produces new capital goods (to be denoted by the subscript ‘cg’). Assume each sector is vertically integrated and thus each one produces its own raw materials.

To begin with, we focus on the supply and demand for wage-goods in any period. This is a useful step towards identifying the relationship between the real wage and the wage share in the wage-goods sector on one hand and the rate of capital accumulation (i.e. the level of investment) on the other.^{Footnote 6}

What can we say about the total supply of wage-goods in any period? Let us approach it this way. The average product of labour in the wage-goods sector (A_wg) will be the ratio of output to labour input

$A_{wg}=\frac{C_{wg}}{L_{wg}}$

where $C_{wg}$ is the supply of wage-goods in real terms.

This implies that the output of wage-goods (I am assuming that this is equal to the quantity of wage-goods supplied to the market) in any period will be

$C_{wg}=A_{wg}{L}_{wg}$

What can we say about the demand for wage-goods? Let w be the money wage per worker (all workers are assumed to be identical so both sectors pay the same money wage to their workers) and $p_{wg}$ be the price of wage-goods (assume all workers consume an identical ‘basket’ of wage-goods). So the ‘real wage’ (measured from the point of view of the worker) is defined as $w/p_{wg}$ and this is the same for all workers.

Now we know that the total money amount spent on wage-goods in this model (total demand for wage-goods) is the total wages bill for the economy (by assumption workers do not save and capitalists do not buy wage-goods), so

$p_{wg}{C}_{wg}=wL$

If the market for wage-goods is in competitive equilibrium,^{Footnote 7} it must be the case that

$p_{wg}{C}_{wg}=p_{wg}{A}_{wg}{L}_{wg}=wL$

Rearranging the above gives an expression for the size of the real wage ( $w/p_{wg}$ – to reduce the amount of notation, I will again write w_r for the real wage) as

(6) $w_r=\frac{w}{p_{wg}}=A_{wg}\left(\frac{L_{wg}}{L}\right)$

In other words, the real wage reflects the average product of labour in the wage-goods sector and the relative size of that sector, as measured by the proportion of the total number of workers who are employed in the sector producing wage-goods.^{Footnote 8}

Now, since total employment will be the sum of employment in the two sectors so that L = L_wg + L_cg, we can write equation (6) as

(7) $w_r=A_{wg}\left(\frac{L_{wg}}{L}\right)=A_{wg}\left(1-\frac{L_{cg}}{L}\right)$

In other words, the real wage reflects the average product of labour in the wage-goods sector and the proportion of the total number of workers who are employed in the sector producing new capital goods.

Notice in passing that equation (7) can be rearranged to yield

(8) $\frac{A_{wg}}{w_r}-1=\frac{L}{L-L_{cg}}-1=\frac{L_{cg}}{L-L_{cg}}=\frac{L_{cg}}{L_{wg}}$

The relationship given in equation (5) implies that

$\frac{A_{wg}}{w_r}-1=\frac{h-h^{*}}{h^{*}}$

Inserting this into equation (8) gives

$\frac{h-h^{*}}{h^{*}}=\frac{L_{cg}}{L_{wg}}$

which is to say that in competitive equilibrium – and thus when profits are being realised – the extent of unpaid labour in the wage-goods sector (and the rate of exploitation) is related to the relative size (as measured by the number employed) of the capital-goods sector.

Equation (7) can also be manipulated to give an expression for the wage share (in the wage-goods sector)

(9) $S_{wg}=\frac{w_r}{A_{wg}}=1-\frac{L_{cg}}{L}=\frac{h^{*}}{h}$

We now introduce the rate of accumulation. The number employed in the capital-goods sector will depend upon the level of output of that sector (I) and labour productivity in that sector (A_cg), such that

$L_{cg}=\frac{I}{A_{cg}}$

Then, equation (7) becomes

(10) $w_r=A_{wg}\left[1-\left(\frac{1}{A_{cg}}\right)\left(\frac{I}{L}\right)\right]$

So the real wage depends upon the average product of labour in the wage-goods sector, the average product of labour in the capital-goods sector and the rate of capital formation per worker in the economy as a whole.

Given the technology in use, the higher the rate of capital formation relative to total employment, the greater will be the proportion of the workforce employed in the capital-goods sector, the lower the proportion of the total workforce employed in the wage-goods sector and thus the lower the output of wage-goods relative to the total number of workers in the economy. The lower, therefore, will be the real wage.

The expression for the real wage (equation (10)) also has implications for the determination of the wage share (aka labour’s share) at least in the wage-goods sector. (I focus on the wage-goods sector because, as we have seen above, it is related to an unambiguous measure of the size of the economic surplus, the rate of exploitation and unpaid labour.) Dividing both sides of equation (10) by the average product of labour in the wage-goods sector (A_wg) gives

(11) $\frac{w_r}{A_{wg}}=S_{wg}=\left[1-\left(\frac{1}{A_{cg}}\right)\left(\frac{I}{L}\right)\right]$

This shows that the wage share in the wage-goods sector and, given equation (5) together with equation (4), the rate of exploitation depends upon two things: first, the pace of accumulation in the economy, specifically (I/L), and second, the average product of labour (i.e. the technique in use) in the capital-goods sector (A_cg).

It is important to note, at least in passing, that in this model, a change in the average product of labour in the wage-goods sector (i.e. technical change in that sector) by itself will not change the wage share or the ratio of ‘paid’ hours to total hours. Essentially, this is because as A_wg changes, the real wage would have to rise in the same proportion (whether as a result of a rise in the money wage and/or a fall in prices) to ensure that the additional output is sold (we are assuming competition – perfectly flexible money wages and/or prices – and market clearing). This is at odds with some sections in Volume 1 of Reference MarxMarx’s (1954) Capital (and especially Chapters 12 and 24), where he typically assumes that ‘real wages … never rise proportionally to the productive power of labour’ (p. 566). If this were the case and the average product of labour in the wage-goods sector were to rise (cet. Par.), the ratio of paid to total hours would fall and the ratio of unpaid to paid hours and thus the rate of exploitation in that sector would rise. This is of some relevance to Australia today, in that unless there is a marked rise in the rate of accumulation at the same time as the real wage is not keeping pace with productivity growth, there will be an excess supply of wage-goods, resulting in falling sales but likely also a fall in orders for stocks and new capital goods, which would contribute to the development of an economic crisis. The reason I am working with a model in which the change in the average product of labour in the wage-goods sector (cet. Par.) is accompanied by a change in the real wage in the same proportion is simply that I am taking Marx seriously when he insists that we must start out by providing an explanation for (the rate of) exploitation consistent with an economy where competition rules and profits are realised (see Note 8).^{Footnote 9}

The evolution of the wage share and the rate of exploitation over time

One of the most important chapters in all three volumes of Capital is the chapter titled ‘The General Law of Capitalist Accumulation’ – this is Chapter 25 of Volume 1. Among the many consequences of capitalist economic growth which he identifies in that chapter, there are two trends that we will consider here: (1) a rise in the ratio of fixed capital to labour and, as a result of this, (2) a fall in the wage share. In this section of the article, we shall use the ideas presented in previous sections to investigate the argument that a fall in the wage share is a necessary consequence of a trend increase in the capital-labour ratio.

Consistent with Reference MarxMarx (1954), I shall assume that the level of investment (i.e. the rate of capital accumulation) is exogenous: ‘To put it mathematically: the rate of accumulation is the independent, not the dependent, variable; the rate of wages, the dependent, not the independent, variable’ (p. 581).

Equation (11) shows that the wage share in the wage-goods sector is negatively related to the rate of accumulation (specifically, I/L) and is positively related to the rate of technical change in the capital-goods sector (i.e. changes in A_cg). We shall discuss the role of each variable in turn.

What can we say about the behaviour of I/L over time? As mentioned above, a key idea to be found in Marx’s Capital is that the capital-labour ratio^{Footnote 10} (K/L) in the economy as a whole will be tending to rise over time. Given this, it is convenient to begin by asking, what must be the behaviour of I/L over time if K/L is rising over time?

For the ratio K/L to rise, the rate of growth of K must exceed the rate of growth of L. In symbols

$\frac{\Delta K}{K}>n$

where n is the rate of growth of total employment, that is, n = ΔL/L.^{Footnote 11}

Neglecting depreciation, the change in the capital stock (ΔK) will equal the ‘value’ (or number) of new capital goods produced in any period, that is, the level of (gross) investment (I). This means we can write the above as

$\frac{I}{K}>n$

which implies that

$\frac{I}{L}>n\frac{K}{L}$

Clearly, given n, if K/L is rising over time, then I/L must be rising over time. As Reference MarxMarx (1959a) puts it, ‘the progress of capital accumulation … goes hand in hand with accelerated accumulation’ (p. 240).^{Footnote 12}

A rising level of I/L implies (given labour productivity in the capital-goods sector) that the wage share in the wage-goods sector would be falling – see equation (11) – and the rate of exploitation would be rising – see equations (4) and (5). However, equation (11) tells us that the wage share does not solely depend on the pace of accumulation (I/L) but also on the average product of labour in the capital-goods sector (A_cg). Reference Blaug and HorowitzMark Blaug (1960) has pointed out that Marx’s work is notable for its ‘persistent emphasis upon technical change as an inherent feature of capital accumulation …’ (p. 495, my emphasis). Given this, it would be unwise for us to neglect technical change and specifically a change (typically for our purposes, a rise) in the average product of labour in the capital-goods sector.

Throughout the discussion which follows, I shall assume throughout that I/L is rising over time and that, at the same time, technical change is going on and A_cg is rising. Equation (11) tells us that the impact of these changes on the wage share will depend upon how large is the rise in A_cg (and thus the fall in 1/A_cg) relative to the rise in I/L.

There are three possibilities.

1. 1. The first possibility is where A_cg is rising, but not as fast as I/L is rising. In this case, the term (1/A_cg) will be falling but at a slower rate than I/L is rising and, as a result, the term $(1/A_{cg})\times (1/L)$ will be becoming larger over time. This will lead to a rise in the proportion of the employees who are employed in the capital-goods sector and this in turn leads to a fall in the wage share and a rise in the rate of exploitation (see equations (4), (5) and (11)).

In their excellent book titled The Political Economy of Marx, Reference Howard and KingMichael Howard and John King (1985) have drawn attention to two things that Marx believed would occur as a capitalist economy experienced economic growth: first that ‘the path of the economy … is one in which Department 1 [the name given by Marx to the sector which produces new capital goods] produces an increasing proportion of total output’ and second that ‘technical change … acts to raise the rate of exploitation …’ (p. 194). This is consistent with the scenario presented in the previous paragraph (where A_cg is rising but not as fast as I/L is rising). However, we cannot rule out a priori either the possibility that A_cg is rising at the same rate as I/L is rising or that it is rising at a faster rate than I/L is rising. We shall look at these two additional possibilities, beginning with the latter case.

1. 2. A second possibility is that A_cg is rising at exactly the same rate as I/L is rising. In this case, the term (1/A_cg) will be falling at the same rate as I/L is rising. This means that will be constant over time and so we can predict that the wage share will be unchanged (see equation (11)). What is the explanation for this? If (1/A_cg) is falling at the same rate as I/L is rising, the proportion of workers employed in the capital-goods industry will be constant over time and so L_wg/L will also be constant. It follows from equations (11), (5) and (4) that the wage share (and the rate of exploitation) will also be constant.

2. 3. A third possibility is that that A_cg is rising faster than I/L is rising. In this case, the term (1/A_cg) will be falling but at a faster rate than I/L is rising and, as a result, the term will be falling over time. In this case, the ratio will be falling over time – as the same output can be produced with fewer workers. This will lead to a rise in the wage share and a fall in the rate of exploitation (again, see equations (4), (5) and (11)).

Notice that for Marx’s prediction – that at the same time as K/L is rising, the wage share will be falling – to hold, we need to assume either that there is no technical change in the capital-goods sector (not a very wise assumption) or that, although there is technical change going on such that A_cg is rising, it is rising at a slower rate than I/L is rising. Only under these assumptions will capital accumulation (specifically, the production of additional capital goods per worker) result in a fall in the wage share – and thus a fall in the ratio between paid and unpaid labour and a rise in the rate of exploitation. However, a priori, I do not see that we can rule out any of the other possibilities but then nor does Marx. In Capital Volume 3, Marx himself recognises that there are various possible outcomes. Considering various things which might offset the tendency for the rate of profit to fall, he writes of the ‘cheapening of elements of constant capital’, by which he means

If we may view the value (i.e. value in terms of labour embodied) of capital goods as being indicated by the ratio $(I/A_{cg})$ – that is, the labour hours required to produce one unit of capital – he is here quite expressly allowing for this ratio to fall or remain unchanged as growth takes place.

Concluding remarks

In this article, I have explored in some detail Marx’s ideas related to the economic surplus, unpaid labour and exploitation. I have attempted to tease out the implications of his analysis for the determination of the wage share.

While I have argued that Marx has not succeeded in providing adequate theoretical support for his prediction in Capital Volume 1 as to the likely behaviour of the wage share as capital accumulates, I hope that I have demonstrated that he has nonetheless provided a very interesting and insightful collection of ideas by which we may, even today, approach a wide range of issues relating to production and distribution.