The Surplus Approach

Abstract

This chapter introduces the surplus approach. The surplus is that part of the social product that is available to the community, or its élite, once it has set aside what is needed to reproduce the same output, that is, for replacement of the means of production and for the subsistence of the working class. The chapter examines some applications of the concept in relation to the birth of ancient civilizations and German mercantilism. Next, it explains the evolution of the ideas of the classical economists and Marx. These economists shared the idea that income distribution depends on power relations between the social classes. A solution to some of the difficulties they encountered was suggested by Piero Sraffa, an economist who was close to Gramsci, Keynes and Wittgenstein. In addition to rediscovering the classical approach, Sraffa also challenged mainstream theory on the basis of analytical problems in its fundamentals. In the 1960s, this criticism led to the so called “two Cambridges controversy”, which involved the brightest economists of the time. The most prominent, Paul Samuelson, admitted that the criticism was correct. Today the controversy is rarely mentioned in university courses, evidently because it has uncomfortable implications for mainstream theory.

Appendices

Appendix

2.1.1 Marx the Transformer

Marx was a great economic scientist and this is evident from how he approached what is known as his “transformation of values into prices”. This problem is also a good exercise in how to “do” economics.

We saw that Marx and Ricardo were aware of the problems of the labour theory of value. In Marx’s terms, if goods were exchanged according to the labour embodied in them, those from “light” sectors that use more living (direct) than dead (indirect) labour (the one incorporated in means of production) would enjoy a higher rate of profit (r) than “heavy” sectors that use more dead than living labour. This is because living and not dead labour is the source of surplus value (i.e. profit). Marx and Ricardo were also both aware that in actual fact, capitalists calculate the profit rate in relation to the total capital they advance, alive or dead, whether in the form of direct or indirect labour. However, Marx does not want to give up the idea that only direct (living) labour gives rise to surplus value. He then strives to prove that although goods are not exchanged according to the principle of embodied labour, surplus value is still only determined by direct labour. Let us see how he reconciles the fact that the rate of profit is actually calculated on variable capital (living labour) as well as constant capital (dead labour) with the idea that its ultimate source is only variable capital.

Marx starts by writing prices as if they were determined by embodied labour. Let us assume (Ricardian vice):

• an economy with only two commodities, corn and steel;

• that the price of a unit of corn is p_c and that of a unit of steel is p_s;

• that for each commodity the unit is chosen so that it incorporates one unit of labour (e.g. if the unit of labour is a labour year, the unit of corn is the quantity of corn such that its production requires 1 year of direct and indirect labour);

• finally, let us assume that in both industries constant capital consists of steel only and variable capital (wages) of corn only.

Using the notation of Sect. 2.12, we write the two labour value/price relations:

$$ \Big\{{\displaystyle \begin{array}{c}{p}_c={c}_c+{v}_c+{s}_c=1\kern0.28em \\ {}{p}_s={c}_s+{v}_s+{s}_s=1\end{array}} $$

(2.6)

In relations (2.6), the price of each commodity is the sum of the labour values, i.e. of the indirect or dead labour contained in the constant capital and of the direct or live labour embodied in the variable and surplus labour (or surplus value) respectively employed in the two sectors. The indirect or “dead labour” used in the two sectors is c_c and c_s, respectively, and the direct or “living labour” is l_c = v_c + s_c and l_s = v_s + s_s, respectively. For instance, c_c is the quantity of labour embodied in the steel used to produce one unit of corn, and v_c + s_c is the live or direct labour employed for the same production. The equality to 1 derives from our choice of the units in which corn and steel are measured.

You will recall that living labour is a source of surplus value because workers use part of their working day to produce that portion of the social product that returns to them as wage-goods (v), whereas for the rest of the day they produce commodities for the master, which are his surplus or surplus value (s). Marx defines the ratio s/v as the “rate of exploitation”, in other words the ratio of the part of the working day that goes to the master to the part that goes to the worker. Assuming a 10-hour working day, if the workers “work for themselves” for 5 hours (producing wage-goods) and for the master for 5 hours (producing the surplus), the resulting rate of exploitation will be s/v = 5/5 = 1 (i.e. 100%). This ratio must be the same in the two sectors (for a given working day), namely:

$$ \raisebox{1ex}{${s}_c$}\!\left/ \!\raisebox{-1ex}{${v}_c$}\right.=\raisebox{1ex}{${s}_s$}\!\left/ \!\raisebox{-1ex}{${v}_s$}\right. $$

(2.7)

It has to be the same, otherwise, the workers would migrate to the sector where they are less exploited, i.e. where for a given working day they receive a higher wage. Competition between workers to work in that industry would lead to a decrease in wage in that industry and a levelling of the rate of exploitation. As with communicating vessels, Marx holds that the rate of profit in the two sectors must also be identical. If commodities are exchanged in proportion to their labour values, we determined the rate of profit using relation (2.5), $r=\raisebox{1ex}{$s$}\!\left/ \!\raisebox{-1ex}{$\left(c+v\right)$}\right.$ (the surplus value or profits divided by the constant and variable capital advanced). Hence the condition for uniformity of the rate of profit in the two sectors is:

$$ {r}_c=\frac{s_c}{c_c+{v}_c}={r}_s=\frac{s_s}{c_s+{v}_s} $$

(2.8)

If you are lucky enough to have a daughter who is a science nerd (if not, you must trust me), you can check with her that we simultaneously have uniformity of the rates of exploitation (relation 2.7) and of the rates of profit (relation 2.8) only if $\raisebox{1ex}{${c}_c$}\!\left/ \!\raisebox{-1ex}{${v}_c$}\right.=\raisebox{1ex}{${c}_s$}\!\left/ \!\raisebox{-1ex}{${v}_s$}\right..$ This ratio, that Marx calls the “organic composition of capital”—i.e. the ratio of the two capital components (constant and variable)—must be the same in both sectors. But this is what we said in words: if commodities are exchanged at their labour values, uniformity of the rate of profit entails that there are no light and heavy sectors: the organic composition of capital must be the same. Since this is impossible, as a true scientist, Marx can only conclude that commodities are not exchanged according to the labour embodied in them.

Now for some numbers. Here is a numerical example of relations (2.6). The numerical values are taken from Garegnani¹³:

$$ \Big\{{\displaystyle \begin{array}{c}{p}_c=1=0.4+0.3+0.3\kern0.28em \\ {}{p}_s=1=0.6+0.2+0.2\end{array}} $$

(2.6’)

The rate of profit in the corn sector is ${r}_c=\frac{s_c}{c_c+{v}_c}=\frac{0.3}{0.4+0.3}=3/7,$ which is different from that in the steel sector, which comes to 1/4. In the lighter sector (corn), it is higher.

Marx then reasons as follows. If capitalists have to obtain the same rate of profit (r), prices should be calculated by applying the latter to all the capital advanced in each sector (respectively c_c + v_c and c_s + v_s). Marx does this with relations (2.9), in which he determines the “prices of production”:

$$ \Big\{{\displaystyle \begin{array}{c}{p}_c=\left({c}_c+{v}_c\right)\left(1+r\right)\kern0.28em \\ {}{p}_s=\left({c}_s+{v}_s\right)\left(1+r\right)\end{array}} $$

(2.9)

Relations (2.9) “transform” labour values (c_c, c_s, v_c and v_s) into prices (p_c and p_s). However, Marx insists that the rate of profit for the economy continues to be calculated on the basis of relation (2.5) [s/(c + v)], where the values of c, v and s for the whole economy are still measured in labour content. The idea that the rate of profit depends on the ratio of the surplus to capital advanced, all measured in labour terms, is thus preserved from the viewpoint of the economy as a whole. The prices of production, calculated with relations (2.9), then have the “democratic” task of making sure the same rate of profit is uniformly applied in the two sectors.

With the above numbers, the general rate of profit calculated with relation (2.5) is

$$ r=\raisebox{1ex}{$s$}\!\left/ \!\raisebox{-1ex}{$\left(c+v\right)$}\right.=\raisebox{1ex}{$0.5$}\!\left/ \!\raisebox{-1ex}{$\left(1+0.5\right)$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right. $$

where s = s_c + s_s = 0.3 + 0.2, etc.

Relations (2.9) become:

$$ \Big\{{\displaystyle \begin{array}{c}{p}_c=\left(0.4+0.3\right)\left(1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)=28/30\kern0.28em \\ {}{p}_s=\left(0.6+0.2\right)\left(1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)=32/30\end{array}} $$

(2.9’)

Before the “transformation”, a unit of corn was exchanged for a unit of steel. Not now! Steel is worth more (32/30 against 28/30 of corn) for a reason. Indeed, the prices of production settle the “unfair” situation in which capitalists in the steel sector obtained a lower rate of profit for labour values.

At this point, Marx perceives a further problem: when capitalists calculate prices of production on the basis of the costs of capital advanced for means of production (c) and for wages (v), they do not calculate these costs at their “labour value”. Indeed, in relations (2.9), we see that the quantities c_c, c_s, v_c and v_s are still “labour values”. But capitalists do not purchase means of production c_c and c_s (for example) at their “labour value”, they buy them at their production price p_c and p_s. With great acumen, Marx then suggests taking this into account and calculating the cost of inputs c_c, c_s, v_c and v_s at their price of production, which amounts to suggesting that relations (2.9) be modified as follows (although he did not attempt to write relations 2.10):

$$ \Big\{{\displaystyle \begin{array}{c}{p}_c=\left({c}_c{p}_s+{v}_c{p}_c\right)\left(1+r\right)\kern0.28em \\ {}{p}_s=\left({c}_s{p}_s+{v}_s{p}_c\right)\left(1+r\right)\end{array}} $$

(2.10)

These equations could be written in this simple form because of two further simplifying assumptions we made to render the problem as simple as possible: constant capital c_c and c_s is multiplied by p_s because we assumed it consists only of steel, and variable capital v_c and v_s is multiplied by p_c because we assumed wages consist of corn.

Marx does not write down these equations, but from his suggestions it seems clear that he believed that since r is determined by relation (2.5) [s/(c + v)], relations (2.10) contains as many unknowns (the prices) as equations (one for each good), and the problem is mathematically determinate (as some of you may remember from school, a system of two equations in two unknowns is solvable, i.e. it allows the two unknowns to be determined.).

However, we can detect a further problem.

Call your scientist daughter. If we set the price of one of the two commodities at one, e.g. p_s = 1, that is, we take steel as a unit of measure (or numeraire)—somewhat as in primitive economies prices were measured in terms of cows or other goods, or so they say—then relations (2.10) are sufficient to determine the remaining two unknowns p_c and r. So relation (2.5), upon which Marx continued to rely to calculate the rate of profit on the basis of the “labour value” of c, v and s, is no longer needed!

Very well, Prof, but relations (2.10) still contain labour value coefficients c_c, c_s, v_c and v_s, which therefore still have a determinant role… In actual fact, they do not! It is not easy to explain why, but let me try.

Consider c_c. This “coefficient of production” represents the quantity of labour needed to produce the quantity of steel necessary to produce a unit of corn. Now a unit of steel was defined above as containing one unit of labour (e.g. a working year). In the example, c_c = 0.4 means that c_c contains 40% of a unit of labour. What changes if I say that c_c = 0.4 means that c_c corresponds to 40% of a physical unit of steel? Nothing, because a physical unit of steel was precisely defined as that containing a unit of labour. Consider v_s which equalled 0.2 in the example. This is the quantity of labour contained in the wage-goods (in our case corn) of the workers employed to produce a quantity of steel that embodies a year of work. Now v_a = 0.2 means that v_a is both 20% of a unit of labour, and 20% of a physical unit of corn (since a unit of corn is defined as that produced with a unit of labour). So we no longer need to measure the coefficients c_c, c_s, v_c and v_s in “embodied labour”—we could, but a “physical” measure would do as well, so “embodied labour” does not play any essential role. Relations (2.10) that we derived are a simplified form of the equations Sraffa finally published in 1960 after drafting them in the second half of the 1930s (actually Sraffa did not start with Marx’s equations; only later did he realise their converging paths).

Prof. but where are wages in relations (2.10)? We already touched on this. Wages are represented by v_c and v_s, the quantity of corn that goes to workers employed in the two sectors, the quantities of wage-corn per unit product. This quantity depends on a technical factor—whether the sector is light or heavy—but also on the hourly wage, measured in corn, of the workers. If we know the wage rate and the production techniques, relations (2.10) suffice to determine the rate of profit and the exchange ratio between the two commodities. With a little patience, we could even demonstrate that wage and rate of profit are in an inverse relation, but that is enough for now.

Further Reading

The two main popular books written by archaeologist Vere Gordon Childe are Childe (1936, 1942). Useful summaries of his theories are Childe (1950, 1957). A portrait of the great archaeologist is in Sherratt (1989). In light of many studies in anthropology and archaeology, the break that Childe and Diamond envisaged between the Neolithic and Urban revolutions and the primitive state of hunter-gatherers must be revised to some extent. In fact, many scholars speak of complex and affluent hunter-gatherer societies, often characterized by strategies aimed at preventing the emergence of élites. The most classic text in this regard is Marshall Sahlins (1972). With the adoption of agriculture in some parts of the world, this primitive Eden was abandoned and part of the population became progressively subjugated to work in favour of an élite, the only true beneficiary of “civilization”. So the reasons for this passage are still much debated. A recent example of the study of the origin of social stratification in ancient civilizations conducted on the basis of the surplus approach is by the distinguished Italian archaeologist, foreign associate member of the American National Academy of Sciences, Marcella Frangipane (2018).

Dennis H. Robertson was famous for his delightful quotes from Alice by Lewis Carroll. What does the organization of economic activity through the market allow us to economize? asks Robertson. And he answers (Robertson 1956, p. 154) by quoting Alice: “‘Oh, tis love, tis love,’ said the Duchess, ‘that makes the world go around’. ‘Somebody said,’ whispered Alice, ‘that it’s done by everybody minding their own business.’ ‘Ah well,’ replied the Duchess, ‘it means much the same thing.’” And so he concludes: “if we economists mind our own business, and do that business well, we can, I believe, contribute mightily to the economizing, that is to the full but thrifty utilization, of that scarce resource Love—which we know, just as well as anybody else, to be the most precious thing in the world”. In other words, Robertson argues that by preaching economic organization based primarily on self-interest rather than altruism, economics encourages society not to dissipate its scarce endowment of virtue. Consequently, the more the economy relies on love, the more it will waste it.

In a recent book, Roberto Marchionatti and Mario Cedrini (2017) challenge this logic by defending an economy based on giving and reciprocity. As I already said, anthropology and archaeology studies suggest that most hunter-gatherer communities were probably egalitarian, not due to inherently good human nature, but through social institutions aimed at suppressing hierarchical behaviour. The distinguished archaeologist Bruce Trigger (2003) wonders whether this is possible or even desirable in more complex societies. Regarding the debate in archaeology and anthropology on the origin of inequality, start with Ames (2013). Marchionatti and Cedrini refer, among others, to Karl Polanyi. Though acute, the latter rejected the surplus approach. I discuss this critically in Cesaratto and Di Bucchianico (2020) where it is argued that study of the different economic formations—from the most ancient, through feudalism, to capitalism—concerns how institutions have organized production and distribution of the surplus.

After the First World War, which ended the era of classical liberalism, economic nationalism took hold again and studies on mercantilism flourished, to which Keynes also dedicated sympathetic pages of his opus magnum, the General Theory (Keynes 1936). He relied on the classic treatise by Eli Heckscher (1935). Charles Kindleberger, a magnificent example of political economist, set out his thesis on the need for an imperial hegemon to act as a stabilizer of the global economy in Kindleberger (1973). This stabilising role relates in particular to supporting global demand through the expansion of its internal market, so that imperial power acts as “buyer of last resort”.

The “Ricardian vice” is examined by Heinz Kurz (2016). The fundamentals of classical theory are discussed in Garegnani (1984). The wage theory of classical economists is well illustrated by Antonella Stirati (1994). I also recommend careful study of the already mentioned booklet by Krishna Bharadwaj (1986). For a development of Sraffa’s suggestion regarding the influence of the interest rate pursued by the central bank on the distribution of income, see Massimo Pivetti (1991).

An introduction to different aspects of Sraffa’s work can be found in Roncaglia (2009). The events leading up to award of the prestigious Swedish gold medal in 1961 are narrated by Arthmar and McLure (2016). Myrdal was later awarded the so-called “Nobel Prize” for economics of the Sveriges Riksbank, the Swedish central bank, one of the few awarded to a non-conformist economist. Nevertheless, Myrdal was in favour of abolition of the prize, as was the ultraliberalist Friedrich Von Hayek (1899–1992). On the spurious nature of the “Nobel Prize” for economics see Henderson (2005).

Why Marx’s labour theory of value is defended by some orthodox Marxists on the basis of elementary errors is well explained by Gary Mongiovi (2002). For a Sraffian criticism of the Law of the tendency of the rate of profit to fall, see Steedman (1977, Chap. 9). I thank Stefano Di Bucchianico for suggestions on some recent Marxist interpretations of the crisis, based on the Law of the tendency of the profit rate to fall.

The question whether or not Sraffa achieved his results independently of Marx is a sensitive political question. Garegnani and Kurz use Sraffa’s unpublished works to demonstrate that far from being inspired by Marx’s labour theory of value, he initially saw this theory as a corruption of the more solid surplus approach, as found in Petty and the physiocrats (and in Ricardo land surveyor). A critical exposition of the different points of view with references can be found in Kurz (2012). The events of the “salary as an independent variable” in the hot years of the workers’ struggles are evoked by Fernando Vianello (2004, pp. 510–12).

Sraffa, one of the greatest intellectuals of the previous century, was obviously in contact with his peers. Andrea Ginzburg (2014, 2016) and Amartya Sen (2003) provide interesting pictures of his relationship with Gramsci and Wittgenstein, respectively. The friendship with Gramsci occurred against the dramatic political and human events of the period. Gramsci died suspecting that the Italian Communist Party had deliberately let him languish in prison. Close to the Communist leader to the end, Sraffa tried to dissuade him from this idea, and after his death there followed a dramatic break between the economist and Tania Schucht, Gramsci’s sister-in-law. At the centre is the story of a letter that Ruggero Grieco, a high communist leader in exile, wrote to Gramsci in 1928, a letter that put him in bad light before the fascist court. Various charlatans accused Sraffa of connivance with the alleged Communist strategy of isolating Gramsci in prison. A more balanced reconstruction of this dramatic and exciting story is by Giancarlo De Vivo (2017). Regarding the letter and more generally the relationship between Sraffa and Gramsci, see also Nerio Naldi (2012, 2020).

On the role of unemployment as a disciplinary tool, it is essential to read the essay by Michal Kalecki (1943), where the Polish economist (1899–1970) explains why capitalism is incompatible with full employment: capitalism could achieve it, but it would make the working class too strong. And if it did so by expanding public spending, it would prefer military spending, because social spending could make the working classes aware that modern society can afford generalized welfare. Pure economic poetry.