At the time Marx studied political economy “classical” economists, most notably Adam Smith and David Ricardo, used a “labor theory of value” to explain prices. So it was only natural for Marx also to base his explanation of prices on the amount of labor time it took to produce different commodities. Adam Smith explained the logic as follows:
In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the only circumstance which can afford any rule for exchanging them for one another. If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days’ or two hours’ labour, should be worth double of what is usually the produce of one day’s or one hour’s labour.
(Smith 1776: Book I, Chapter 6, paragraph 1)
However, when classical economists initially developed a labor theory of value to explain relative prices they did not have all the mathematical tools at their disposal we have today. Now we know how to systematically calculate the amount of labor time it takes, both directly and indirectly, to produce goods and services in an economy where goods are produced by labor using other produced goods from a description of the technologies being used. Let a(ij) represent the amount of good i required to produce a unit of good j. And let L(j) be the number of hours of “direct” labor required to produce a unit of good j. In a two good economy we might have the following “recipes” for making each good:
a(11) = .3 a(12) = .2
a(21) = .2 a(22) = .4
L(1) = 1.0 L(2) = .5
The first column is the “recipe” being used to make good 1. It takes workers in the industry producing the first good 1 hour working with 0.3 units of good 1 itself and 0.2 units of good 2 to produce 1 unit of good 1. It can help to think of the 1 hour of “direct labor” as the “stirring time” to transform the “ingredients,” 0.3 units of good 1 and 0.2 units of good 2, into 1 unit of good 1. The second column is the “recipe” for making good 2. It takes workers in the second industry 0.5 hours working with 0.2 units of good 1 and 0.4 units of good 2 itself to produce 1 unit of good 2. The a(ij)s and L(j)s represent the technology of the economy, which is sometimes convenient to represent as {A,L} where the A includes all of the a(ij)s and L includes all the L(j)s.
Notice we are assuming there is only one “primary” input in production, labor. Everything is ultimately made by labor and labor alone. Yes, to make good 1 we need some of good 1 itself and some of good 2 along with labor – that is what the recipe for making good 1 says. But these inputs of goods 1 and 2 were, in turn, produced by labor. In chapter 5 we consider what happens when some other non-produced input from “nature” is required to produce things along with labor. But for now, we assume labor is the only non-produced input in our economy. Moreover, we also assume labor is “homogeneous.” That is, there are not different kinds of labor – carpenters and welders, for example – where production sometimes requires one kind of labor and not the other. Again, we will discuss what happens if we relax this assumption later, but for now we are simply establishing a suitable mathematical framework to represent the thinking of classical economists, including Marx, when they developed the labor theory of value.
Given the above technological data how can we calculate the number of hours it takes not only directly to make a unit of good j, that is L(j), but also the number of hours it took to make the amount of good 1 we need and the amount of good 2 we need to make a unit of good 1, referred to as the time it took to make a unit of good 1 indirectly?
Define V(j) as the number of hours of labor needed both directly and indirectly to make a unit of j. In other words, define V(1) and V(2) as the answers we are seeking. Now ask: How many hours did it take to make a(ij)? By definition it takes V(i) hours in grand sum total to make 1 unit of good i. So it must take V(i)a(ij) hours to make a(ij) units of good i. We can now write what are called the “value equations” for the economy:
(1) V(1) = L(1) + V(1)a(11) + V(2)a(21)
(2) V(2) = L(2) + V(1)a(12) + V(2)a(22)
The first equation says: The number of hours it takes in grand sum total to make 1 unit of good 1, V(1), equals the hours of direct labor, L(1) (stirring time, if you will) plus the number of hours it took to make a(11) units of good 1, plus the number of hours it took to make a(21) units of good 2 (the time it took to make the ingredients). The second equation says the same for good 2. Since all of the a(ij)s and L(j)s are “givens,” i.e. they are simply the description of the technologies being used, {A,L}, there are only two unknowns, V(1) and V(2). While we cannot solve equation 1 without knowing the value for V(2), and we cannot solve equation 2 without knowing the value of V(1), we can solve the two equations simultaneously to obtain mutually consistent values for V(1) and V(2).
In this book we will only encounter equations which can be solved as long as there are as many equations as there are unknowns. So counting equations and unknowns will be important. Fortunately in the case of our value equations there are two equations and two unknowns, and we are able to solve for the values of the two unknowns, V(1) and V(2). The important point is that the technological data – all the a(ij)s and L(j)s which we represent by {A,L} – are sufficient to calculate the labor values in our economy, the V(j)s, which we can represent by V. Symbolically: {A,L} → V.
Substituting the numerical values above into our value equations gives:
V(1) = 1 + .3V(1) + .2V(2)
V(2) = .5 + .2V(1) + .4V(2)
Which can be solved to give: V(1) = 1.842 and V(2) = 1.447.
So what does the above quotation from Adam Smith imply the price of good 1, p(1), and the price of good 2, p(2), should be? The prediction is that the price of good 1 relative to the price of good 2, p(1)/p(2), should be equal to the value of good 1 relative to the value of good 2, V(1)/V(2), i.e. that prices in our economy should be proportional to the number of hours it took in grand sum total to make each good. Symbolically we write this as P ∝ V where P represents the price system and V represents the value system. And in our particular case: V(1)/V(2) = 1.842/1.447 = 1.273, and therefore a unit of good 1 should exchange for 1.273 units of good 2, i.e. p(1)/p(2) should also be equal to 1.273. Notice that our calculation takes into account a complication Smith did not raise in the quotation above: If a beaver hunter needs a trap, which takes someone time to produce, and a deer hunter needs a bow, which takes someone time to produce, we will have taken that into account as well.
Where Marx believed he had surpassed his predecessors was in discovering an explanation for the origin of capitalist profits even when all goods exchange according to the number of hours it takes to make them, both directly and indirectly.1 Marx argued that what his predecessors had failed to notice was that in the case of one special commodity, labor power, the amount of labor time it takes to produce it, and therefore its exchange value, is less than the value it confers on the goods it produces when used. Marx argued that this was the answer to the mystery of why profits are positive even when capitalists pay the full “value” for all inputs and receive no more than the “value” for their products.
Consider a capitalist producing shirts: He begins with a certain amount of money which he uses to purchase cloth from a capitalist in the textile industry, sewing machines from their manufacturer, and hire “labor power” to work with the sewing machines to turn the cloth into shirts, which he then sells. Assume that everything is bought and sold according to the number of hours it took to make it, both directly and indirectly, that is according to what Marx called its “exchange value.” And for convenience, assume a sewing machine lasts only one year. If it took 50 hours (directly and indirectly) to make the sewing machines that is what the shirt capitalist pays for them. If it took 30 hours (directly and indirectly) to make the cloth that is what the shirt capitalist pays for it. And if it took 20 hours to turn the cloth into shirts using the sewing machines, then the shirt capitalist will be able to sell however many shirts were made for 50+30+20 = 100.
But how much will the shirt capitalist have to pay for the 20 hours of labor power he hired? If the economy is productive it does not take a full hour to produce enough wage goods to keep a worker alive and working for an hour. Therefore, even if the capitalist pays for the 20 hours of labor power according to their full value – the number of hours (both directly and indirectly) it took to “produce” them – that will be less than 20 hours. Suppose, for example, that amount is 15 hours. In this case the shirt capitalist’s costs will be 50+30+15 = 95 when he pays the full value for all inputs, including labor power. Since his revenues will be 50+30+20 = 100 when he sells the shirts for their “value,” his profits will be 100−95 = 5.
At this point Marx had achieved his two primary goals: (1) He had an explanation for prices that was very much in line with everyone else’s explanation at the time, namely that relative prices reflect different amounts of labor time needed, both directly and indirectly, to produce commodities. And unlike those writing before him (2) Marx had explained the origins of capitalist profits: Even when commodities sell according to this principle, even when all commodities sell at their “exchange values,” capitalists receive profits because if the economy is productive it takes less than an hour (both directly and indirectly) to produce the bundle of wage goods needed to keep a worker alive and working an hour, i.e. the “exchange value” of labor power is less than the value labor power imparts when used. Voila! We are at the end of Volume I of Capital.2
However, there were two problems. (1) It turns out that prices will not be proportional to labor values in capitalism.3 Moreover, (2) the size of a capitalist’s profits depends on the amount he spends on all inputs, not just how much he spends purchasing labor power, i.e. the size of his wage bill. We take up the first problem later in this chapter and leave the second problem to chapter 2 where we discuss profits. But first, let’s see how Sraffians explain prices under capitalism.
Assume the same two good, two industry economy as before:
a(11) = .3 a(12) = .2
a(21) = .2 a(22) = .4
L(1) = 1.0 L(2) = .5
Let p(i) be the price of a unit of good i, w be the hourly wage rate, and r(i) be the rate of profit received by capitalists in sector i. The first step is to write down an equation for each industry that expresses the truism that revenue minus cost for the industry is, by definition, equal to industry profit. If we divide both sides of this equation by the number of units of output the industry produces we get the truism that revenue per unit of output minus cost per unit of output must equal profit per unit of output. Another way of saying this is: cost per unit of output plus profit per unit of output must equal revenue per unit of output. This is the equation we want to write for each industry.
The second step is to write down what cost per unit of output and revenue per unit of output will be for each industry. For industry 1 it takes a(11) units of good 1 itself to make a unit of output of good 1. That will cost p(1)a(11). It also takes a(21) units of good 2 to make a unit of output of good 1. That will cost p(2)a(21). So [p(1)a(11) + p(2)a(21)] are the non-labor costs of making one unit of good 1. Since it takes L(1) hours of labor to make a unit of good 1 and the wage per hour is w, the labor cost of making a unit of good 1 is wL(1). Revenue per unit of output of good 1 is simply p(1).
What is profit per unit of output in industry 1? By definition profits are revenues minus costs, so profits per unit of output must be equal to revenues per unit of output minus cost per unit of output. Also by definition the rate of profit is profits divided by whatever part of costs a capitalist must pay for in advance. Dividing both the numerator and denominator by the number of units of output in industry 1 gives us the truism that the rate of profit in industry 1 is equal to the profit per unit of output in industry 1 divided by whatever part of costs per unit of output capitalists must advance in industry 1. Therefore, the profit per unit of output in industry 1 must be equal to the rate of profit for industry 1 times the cost per unit of output capitalists must advance in industry 1.
Assume that capitalists must pay for all costs in advance.4 So the cost per unit of output capitalists must advance in industry 1 is [p(1)a(11) + p(2)a(21) + wL(1)]. Also assume that the rate of profit capitalists receive is the same in both industries, r, since otherwise capitalists would move from industries with a lower rate of profit to industries with a higher rate of profit until their profit rates became the same.5 Therefore:
profit per unit of output in industry 1 = r[p(1)a(11) + p(2)a(21) + wL(1)]
And we are ready to write the accounting identity, or truism, that cost per unit of output plus profit per unit of output equals revenue per unit of output in industry 1:
[p(1)a(11) + p(2)a(21) + wL(1)] + r[p(1)a(11) + p(2)a(21) + wL(1)] = p(1)
Which can be rewritten as: (1+r) [p(1)a(11) + p(2)a(21) + wL(1)] = p(1). Writing a similar equation for industry 2 we get what are called the “price equations” for the economy:
(3) (1 + r) [p(1)a(11) + p(2)a(21) + wL(1)] = p(1)
(4) (1 + r) [p(1)a(12) + p(2)a(22) + wL(2)] = p(2)
The price equations are 2 equations with 4 unknowns: w, r, p(1), and p(2). (Recall the a(ij) and L(j), i.e. {A,L}, are technological “givens.”) But we are only interested in relative prices, i.e. how many units of one good trade for how many units of another good. If we set the price of good 2 equal to 1, p(2) = 1, then p(1) tells us how many units of good 2 one unit of good 1 exchanges for, and w tells us how many units of good 2 a worker can buy with her hourly wage. So we now have 2 equations in 3 unknowns: w, the “real” hourly wage rate, r, the uniform rate of profit in the economy, and p(1), the price of good 1 relative to the price of good 2. We do not have as many equations as unknowns, and therefore cannot solve yet for the values of our unknowns.
However, we can ask: What would r and p(1) in this economy be if the wage rate were, for example, w = 0.691? In which case we simply substitute w = 0.691 and p(2) = 1, along with the data representing our technologies (or recipes) for producing the two goods, into the two price equations and solve for p(1) and r. Solving:
(1 + r)[.3p(1) + .2(1) + 1(.691)] = p(1)
(1 + r)[.2p(1) + .4(1) + .5(.691)] = 1
Gives: p(1) = 1.273 and r = 0.
And we can ask: What if the conditions of class struggle are such that workers’ wage is only 0.500 units of good 2 per hour? What will p(1) and r be? Solving:
(1 + r)[.3p(1) + .2(1) + 1(.500)] = p(1)
(1 + r)[.2p(1) + .4(1) + .5(.500)] = 1
Gives: p(1) = 1.190 and r = .126 or 12.6%.
And we can ask: If the conditions of class struggle are such that workers only receive w = 0.400, what will p(1) and r be? Solving:
Gives: p(1) = 1.137 and r = .208 or 20.8%
In our example, as the wage rate falls from 0.691 to 0.500 to 0.400 units of good 2 per hour, the rate of profit rises from 0% to 12.6% to 20.8%. It is possible to prove that this negative relationship always holds, but we leave discussion of how wage rates and the rate of profit are determined according to Sraffian theory to the next chapter. In this chapter we are concerned with explaining prices. In all cases we set p(2) = 1, making good 2 what is called our “numeraire,” so as explained p(1) represents how many units of good 2 one will get in exchange for a unit of good 1, and w represents how many units of good 2 a worker can buy with her hourly wage. Notice what we have discovered so far:
• As we change from one possible combination of (w, r) to another, that is from (w = 0.691, r = 0.00) to (w = 0.500, r = 0.126) to (w = 0.400, r = 0.208), p(1), the price of good 1 relative to good 2, changes from 1.273 to 1.190 to 1.137 even though production technologies are the same in all three situations. Clearly relative prices are not determined by technology alone. Clearly income distribution plays a role in price determination.
• Only in the case where r = 0 is p(1) = 1.273. So only in the case where r = 0 are relative prices proportional to the labor values of the two goods. Whenever r is different from zero relative prices are no longer proportional to labor values, but deviate systematically from labor values.6
What at first appears to be a big difference between the two explanations of prices, in fact is not. It appears that the Marxian theory of prices is determinate while the Sraffian theory is not. According to Sraffian theory we cannot determine what relative prices and the rate of profit will be until we know what the wage rate is. On the other hand, in the Marxian system it appears we have an immediate answer to what relative prices and the rate of profit will be without need for more information – even if we have to make some sort of technical adjustment to “transform” labor value prices into “prices of production” to make those prices consistent with equal rates of profit in all industries, as we will soon discuss. But in fact, both systems are equally determinate, or indeterminate.
To make the Sraffian explanation of relative prices and the rate of profit determinate all one has to do is stipulate a given real wage rate, w. Moreover, the only reason the Marxian theory gives an immediate answer to what prices and the rate of profit will be is that Marx implicitly specified a real wage rate when he assumed that labor power will exchange according to the number of hours it takes (both directly and indirectly) to produce a particular wage bundle, in his case the bundle sufficient to keep a worker alive and working for an hour, i.e. a subsistence real wage. In short, in neither theory is it possible to derive relative prices and the rate of profit until a real wage rate has been stipulated. In both Marxian and Sraffian theory a real wage must be stipulated before relative prices and the rate of profit can be derived.7
However, there is a major difference between the Sraffian and Marxian theories of prices under capitalism. Marxian theory starts with technology, derives labor values, and then, as we will soon see, must “transform” these labor values into what Marxists call “prices of production” which are consistent with equal rates of profit in all industries. In other words the process is: {A,L,ws} → V → P where ws stands for a subsistence wage rate. Whereas Sraffian theory derives prices consistent with equal rates of profit in all industries directly from technologies and a given real wage: {A,L,wa} → P where wa stands for any wage rate workers manage to achieve.
First, it is well known that it is possible to go from V → P. It is also well known that Marx’s suggestion for how to perform this calculation, i.e. how to “transform values into prices of production” in Chapter IX of Part II of Volume III of Capital does not work.8 But it is also well known that many others, beginning with Ladislaus Bortkiewicz in 1906, have derived algorithms which begin with V and successfully end up with P. Since P is a relative price vector while V is a vector of absolute values, there is one degree of freedom when performing the transformation. This has given rise to many different “solutions” to the transformation problem depending on one’s choice of how to turn the relative price system into an absolute price system, i.e. on choice of a numeraire. And much ink has been spilled among Marxist economists debating over which choice of a numeraire is “more consistent” with Marx’s argument, or intent, which choice “better illustrates” some valuable lesson about how capitalism functions, etc. But the question is: Why bother? If we can derive prices of production directly from technologies for any real wage – as Sraffian theory demonstrates we can – why bother first to calculate labor values, only to have to go to the trouble of deriving a correct set of prices starting from labor values?
I am not the first to ask this question and suggest that we should not go to the extra trouble. Eugene Bohm-Bawerk pointed out in Karl Marx and the Close of His System published in 1896, two years after Volume III of Capital was published in 1894, that the theory of value from Volume I was redundant since the prices of production Marx derived in Volume III could be correctly determined without reference to labor values. Paul Samuelson made this point in a particularly poignant way:
I should perhaps explain in the beginning why the words ‘so-called transformation problem’ appear in the title. As the present survey shows, better descriptive words than ‘the transformation problem’ would be provided by the ‘problem of comparing and contrasting the mutually-exclusive alternatives of “values” and “prices”.’ For when you cut through the maze of algebra and come to understand what is going on, you discover that the ‘transformation algorithm’ is precisely of the following form: ‘Contemplate two alternative and discordant systems. Write down one. Now transform by taking an eraser and rubbing it out. Then fill in the other one. Voila! You have completed your transformation algorithm.’
(Samuelson 1971)
However, before citing Occam’s razor and declaring discussion closed because prices under capitalism can be explained without referring to labor values, and are not equal to labor values in any case, we should consider if there is any reason why beginning with labor values on our way to explaining prices might be insightful. Is there something we learn from doing so, something we might otherwise fail to understand? Over the years various Marxist economists have suggested different rationales for defining and using labor values to understand how capitalist economies function. They fall into four categories:
1. In capitalist economies values originate first, and subsequently become transformed into prices. In other words, our intellectual transformation reveals something important about the actual process of price formation in capitalist economies.
2. A transformation from value prices to prices of production occurs when a pre-capitalist market economy Marx called “simple commodity production” is transformed into a capitalist economy. In other words, our intellectual transformation mirrors a hypothetical, or perhaps an actual historical, transformation, from one kind of economic system to another.
3. Labor values are necessary because otherwise the origin of profits will remain a mystery.
4. Capitalism is best understood by studying production first and exchange second, and values are needed to understand production, while prices of production are only necessary to understand exchange.
We consider the first two rationales here and leave the last two rationales until the next chapter when we compare Marxian and Sraffian theories of profits.9
The “transformation problem” is this: If profits come only from the part of financial capital one advances to hire labor power, if capitalists in different industries distribute the portion of the capital they advance between labor power (their wage bill) and produced inputs they purchase from other capitalists (their non-labor costs) differently, and if goods sell at their values; then capitalists in different industries will have different rates of profit.10 To see this, return to our earlier example, remembering that for convenience we are assuming that machines last for only one year:
Our shirt capitalist advanced 50 for sewing machines + 30 for cloth + 15 for labor power = 95 in total, and he sold the shirts produced by 20 hours of labor power for (50+30+20) = 100, which yielded profits of 5. So the shirt capitalist’s rate of profit was 5/95 = .05263 = 5.263%.
Now consider a steel capitalist who pays 100 for steel making machines (blast furnaces and rolling mills) because that was the number of hours it took to produce them, both directly and indirectly, 60 for iron ore and coal, because that was the number of hours it took to produce them, both directly and indirectly, and 15 for 20 hours of labor power, which he then puts to work with his machines and ore producing steel. The steel capitalist will be able to sell the steel for 100+60+20 = 180. His cost is 100+60+15 = 175, so his profit is also 5. However, his rate of profit is only 5/175 = .02857 = 2.857%. What are we to make of this? There are four possible responses.
(1) The rate of profit in the steel industry will be lower than the rate of profit in the textile industry. Since it is a well-known fact that in the real world capitalists in different industries do, in fact, often earn different rates of profit, perhaps we have discovered the reason why.
However, all concerned – Marx, Marxians, Sraffa, Sraffians, and mainstream economists alike – all reject this response to our finding. What is agreed by all concerned is that different rates of profit among industries which are not transitory are due to barriers to the mobility of financial capital – because otherwise capitalists would withdraw their financial capital from low profit industries to invest instead in high profit industries until discrepancies in profit rates were eliminated. Moreover, there is no evidence whatsoever that higher rates of profit are correlated with a higher proportion of expenditures on labor compared to non-labor inputs. If anything, higher rates of profit seem empirically to correlate with more capital intensive industries, precisely because they are often characterized by higher barriers to entry.
(2) Clearly the problem arises because steel capitalists only spend 15/175 = .08571 = 8.571% of their financial capital on labor power, i.e. steel capitalists have what Marx called a high “organic composition of capital.” While textile capitalists spend 15/95 = 0.15789 = 15.789% of their financial capital on labor power, i.e. textile capitalists have a low organic composition of capital. The second possible response is to conclude that absent barriers to entry capitalists will move their capital from the steel industry (where profits are initially lower) to the textile industry (where profits are initially higher) until the organic compositions of capital become equal in the two industries. Various critics of Marx, including Bohm-Bawerk (1949) and Vilfredo Pareto, have interpreted Marx as suggesting that this is, in fact what happens.
However, most Marxists agree with Ronald Meek (1973) that there is ample evidence that this is not what Marx suggested would happen. In any case, there is no reason to believe that if a capitalist moves his financial capital out of steel into textiles this would affect the organic composition of capital in either industry. The organic composition of capital in an industry is determined by whatever is the cost minimizing technology for that industry. When a new capitalist invests financial capital in the textile industry he would presumably invest 15.59% of his financial capital in labor power, just as other textile capitalists do, and capitalists left in the steel industry would continue to invest only 8.571% of their financial capital in labor power.
(3) A third response is that absent barriers to movement financial capital will move from low to high profit industries without changing the organic compositions of capital in either industry, but instead leading to changes in the prices at which goods sell, i.e. it leads to a modification, or “transformation,” of initial labor value prices into “prices of production” which are consistent with a uniform rate of profit in all industries. In other words, rather than affect compositions of capital, the movement of financial capital between industries brings about a change in the prices of the goods they produce which initially sell at their values but then sell at somewhat different “prices of production.” As financial capital flows out of steel this raises steel’s “price of production” above its labor value so as to increase the rate of profit in the steel industry; and as financial capital flows into textiles it lowers textiles’ “price of production” below its labor value to lower the rate of profit in the textile industry. In this interpretation rates of profit become equalized in the two industries by modifications of their selling prices, not by changes in their compositions of capital. At least in the following passage, it seems that this is what Marx had in mind:
Now if the commodities are sold at their values, then, as we have shown, very different rates of profit arise in the various spheres of production, depending on the different organic composition of the masses of capital invested in them. But capital withdraws from a sphere with a low rate of profit and invades others, which yield a higher profit. Through this incessant outflow and influx, or briefly, through its distribution among the various spheres, which depends on how the rate of profit falls here and rises there, it creates such a ratio of supply to demand that the average profit in the various spheres of production becomes the same, and values are, therefore, converted into prices of production.
(Marx, Capital, Volume III: 195–196)
And it is the interpretation favored by Anwar Shaikh (1977: 134) who argued: “The transformation procedure as set out by Marx reflects the inherent nature of the process of the equalization of profit rates. This is a continuously occurring process, and in its pure form it acts by changing prices of individual commodities while leaving the sum of prices of a given mass of commodities intact.”
The problem with this interpretation is there is no evidence of financial capital constantly flowing from capital intensive industries to labor intensive industries to transform labor value prices into prices of production. There is no empirical evidence of any “incessant outflow and influx” and the only reason we need to believe in such a flow is that we started from the assumption that goods initially tend to sell according to their labor values. If we drop the assumption that prices in capitalism tend to be equal to labor values initially we don’t need to search for a pattern of financial capital flows that nobody has ever seen.
(4) The fourth possibility is that there is no initial tendency for prices in capitalism to be equal to labor values, i.e. prices in capitalism are never equal to labor values. Instead what free mobility of financial capital between industries, or the threat of mobility, does is lead directly to the formation of prices which are systematically different from labor values which yield equal rates of profits in all industries.
Indeed, in other passages Marx himself seems to realize this, even if only in a somewhat confused way:
As soon as capitalist production reaches a certain level of development, the equalization of the different rates of profit in individual spheres to a general rate of profit no longer proceeds solely through the play of attraction and repulsion, by which market prices attract or repel capital. After average prices, and their corresponding market prices, become stable for a time it reaches the consciousness of the individual capitalists that this equalization balances definite differences, so that they include these in their mutual calculations. The differences exist in the minds of the capitalists and are taken into account as grounds for compensating. (italics in the original)
(Marx, Capital, Volume III: 209)
Only if one begins with a belief that some capitalists are prone to have higher profit rates than others because they spend a higher proportion of their financial capital on labor power is there any need to worry about something reaching the “consciousness” of capitalists, or capitalists discovering an equalization to balance “definite differences” – whatever that may mean.
Indeed, the solution is quite simple: Free mobility of financial capital leads directly to the formation of what Marx called prices of production. There is no tendency for labor value prices to form in the first place. In capitalist economies labor value prices do not appear first, and then require transformation into prices of production. Capitalists who spend a higher proportion of their financial capital on labor are not prone to higher rates of profit than those who spend a higher proportion on non-labor inputs. Free mobility of financial capital in a competitive capitalist economy renders all inputs to production equally “exploitable” as evidenced by the ability of all capitalists to mark-up an equal amount on all forms of costs, regardless of whether they are labor costs or non-labor costs. However, this simple, and rather obvious solution is the Sraffian solution, and implies that labor values are redundant, if not misleading, in explaining price formation in capitalism.
But what about the second rationale for studying labor values? Are not labor values necessary in order to understand the difference between price formation in a pre-capitalist market economy and price formation in a competitive capitalist economy? This argument has much more to recommend it. Indeed, one important thing to understand about different economic systems is why they generate different price signals, even if their technologies, resource endowments, and consumer preferences are the same.
As long as we do not attempt to use labor values to explain prices in capitalist economies, there is no reason they may not be helpful in explaining price formation in some other economic system, such as the one Smith alluded to as an “early and rude state of society” and Marx called “simple commodity production.” The defining characteristic of such a system is the absence of employers and employees. There are no employers seeking the highest rate of profit available as they hire employees to work with inputs they provide. There are no employees who lack the necessary wherewithal to produce themselves, and who therefore have no choice but to hire themselves out to capitalists for an hourly wage. There are only self-employed producer/consumers who may from time to time exchange commodities with one another.
However, even in such an economy notice there is an implicit assumption that every deer hunter could just as easily (and happily) trap beaver if he so chose; and every beaver trapper could just as easily (and happily) hunt deer if he so chose. Because only then if it takes twice as much time to trap and skin a beaver as kill and dress a deer would no deer hunter ever accept less than 1 beaver pelt for 2 deer, and no beaver trapper accept less than 2 deer for 1 beaver pelt. In sum, labor values may well be a useful way to understand relative prices in some non-capitalist economy under some very stringent and unrealistic assumptions, even if they are not helpful for understanding price formation in capitalist economies.
1 Like many others, Marx was fully aware that profits sometimes derive from “buying cheap and selling dear.” But Marx realized that while this may explain why a particular capitalist achieved positive profits, it does not explain why capitalist profits would be positive in general, or on average. And Marx correctly surmised that even if no capitalist ever “bought cheap and sold dear,” i.e. that goods always sold at their “values,” capitalist profits would be positive.
2 By this I do not mean to imply that people should not bother to read volume 1 of Capital – far from it. It is a truly transformative experience I recommend for everyone. Volume I is well worth reading for the historical information it contains about the deplorable working and living conditions endured by the working classes during Britain’s industrialization under capitalism, and for the indignation and outrage that leaps from Marx’s pen. I am simply saying that the formal model and the conclusions based on it which Marx develops in Volume I reduce to the summary I have provided here.
3 Not only Marx, but before him David Ricardo and even Adam Smith were aware of this problem, which we take up below.
4 When writing the price equations for the economy Sraffa and his followers usually assume that capitalists must pay only for non-labor inputs in advance, and can pay their employees out of the revenue from current sales. However, since we are comparing Sraffian theory with Marxian theory we make the same assumption here as Marx and his followers, namely that capitalists must pay for labor as well as all non-labor inputs in advance.
5 In effect we are assuming there are no barriers to entry or movement of financial capital from one industry to another, and engaging in what Kurz and Salvadori (1995) call “a long-period analysis.” Marxians (with a few notable exceptions) and Sraffians both conduct their analysis at this level of abstraction.
6 For proof that these results always hold in a more general Sraffian model see theorem 13 in Hahnel 2017.
7 We leave discussion of the similarities and differences between Marxian and Sraffian explanations for the real wage to next chapter. But it is worth noting here a crucial difference between “classical” and “neoclassical” explanations of price and income determination. Both Marxian and Sraffian “classical” explanations of prices and profits require a prior determination of the wage rate. Moreover, in neither of these classical theories is the wage rate determined entirely by the marginal productivity of labor, or the rate of profit determined by the marginal productivity of something called “capital,” as they are in neoclassical theory.
8 Anwar Shaikh (1977) demonstrated that while Marx’s solution does not work, if we treat Marx’s attempt as merely the first step in an iterative process, and do perform the operation Marx did over and over again, we can eventually arrive at the correct prices of production.
9 There is a fifth reason to define labor values which does, indeed, prove useful to understanding one reason capitalist economies cannot be trusted to achieve “dynamic efficiency.” However, since Marxists have little interest in whether or not the capitalist price system accurately represents social opportunity costs, ironically this rationale for defining and using labor values is not one Marxists have emphasized. In any case, we will put labor values to good use in chapter 3 when we analyze technological change and “dynamic efficiency” in a Sraffian framework.
10 Paul Sweezy explained the problem as follows: “According to the theory of Volume I, commodities exchange in proportion to the quantity of labor (stored-up and living) embodied in them. Surplus value (or profit), however, is a function of the quantity of living labor alone. Hence, of two commodities of equal value one with relatively more living labor will contain more surplus value than one with relatively more stored-up labor; and this implies that equal investments of capital will yield different rates of profit depending on whether more or less is put into wages (living labor) on the one hand or material accessories (stored-up labor) on the other. But this theory contradicts the obvious fact that under capitalism equal investments, regardless of their composition, tend to yield equal profits.” Introduction to Bohm-Bawerk 1949: xxiii.