So I promised everyone a thread about Marx's central thesis of "the tendency of the profit rate to fall". It's been a couple months since I read that portion of Capital Volume 3, so bear with me.

Let's begin with some of the things laid down in Capital Vol. 1.
You need to first understand the basics of the Labor Theory of Value to understand how he builds on it in later volumes.

First we need to define the terms:

"constant capital" refers to the means of production, raw materials (and the value or "dead labor" they include.
For instance, if a carpenter is working with lumber to craft chairs, that lumber already has a certain amount of "dead labor" in it - labor had to take place to cut down those trees, trim them, transport them, etc. - all of that is included in the value of the raw materials.)
"constant capital" also includes the value of the tools used, the cost of replacing them when they break, the cost of upkeep of the machinery and buildings used, the depreciation in the value of those machines, buildings, etc.
In Vol. 2, he explains that "constant capital" can be divided into two parts - "fixed capital" and "circulating capital". "Fixed capital" represents the parts of constant capital which have to be replaced only every once in a while - like machinery, buildings, etc.
To replace this "fixed capital", and thus keep the business running, the capitalist must set aside a portion of his revenue in a savings account, so that when the time comes to replace these costly things, that money is readily available.
The other half of "constant capital" is "circulating capital". This represents the raw materials which have to be replaced/provided anew every time a cycle of production takes place. This can include tools which are used only once, like nails, for instance.
Constant capital also includes the costs of shipping finished commodities to the market, paying merchants/salesmen, cashiers, janitors, supervisors - basically, everything and everyone that isn't directly involved in the process of producing commodities, but which are essential.
So that covers the term "constant capital".

The next term we need to define is "variable capital".

This one's really simple. It's just the wages paid to the workers involved directly in the production of commodities.
The next term we need to define is "surplus-value"

"Surplus-value" is the value produced by the workers directly involved in production over and above the wages they are paid. This surplus-value only exists in the commodity form until those are sold.
So in other words, the "surplus-value" comes from the unpaid portion of the workers' pay, and first takes the form of "commodity capital". Once that commodity capital is sold on the market, the entire value of the commodities, including the surplus-value is "realized".
By "realized", he means "changed from commodity capital into money capital".

So let's first look at the formula for Capital itself:

M = (C+v)+S=V = M'
I'll break this down:

Money Capital is invested in constant and variable capital. When production takes place, surplus-value is added by the unpaid labor of workers. The value of the constant and variable capital + the surplus-value = the Value of the finished product.
When that Value (in the form of commodity capital) is "realized" in the market (when the commodity is sold), the commodity capital becomes Money Capital once again, as at the beginning of the process, + an added value, or "surplus-value" - thus, M', or M+added value.
This whole process can be simplified in the following way:

M-C-M'

When Money Capital increases the value of itself through the process of production and distribution, this process is known as "valorization". Money IS NOT CAPITAL UNLESS IT INCREASES ITS VALUE.
That's what Capital IS - the process of spending money with the sole purpose of increasing its value. Capital isn't a THING, it's a PROCESS.

All commodities possess two values within them - "use value" and "exchange value".

Capital is completely focused on exchange value.
As opposed to this previously mentioned process -

M-C-M' (quick caveat I forgot to mention - the "C" in this stands for the commodities the capitalist spends Money Capital on in the production process - constant capital, and variable capital, or wages),,,
there is another, diametrically opposed process which can also take place.

C-M-C

This is the process that the working class is stuck in - they exchange the only commodity they have readily available - their labor-power - for money, and exchange that for commodities to live on.
Now let's consider for another moment the process M-C-M'.

It wouldn't make any sense for you to exchange $1 for a commodity worth $1, and then exchange that for another $1, right? (M-C-M) That would be stupid, and pointless. But C-M-C is what WE have to do to simply keep living.
Notice how the C-M-C process the working class is stuck in doesn't include any extra value at the end of the process. Due to some fundamental rules that the capitalist system has to adhere to in order to function (beyond the scope of this investigation,
workers' wages are always kept as near as possible to the bare minimum required for us to not only survive, but to keep on being productive workers - and NOTHING more. This "minimum basic standard" of living changes over time, given the material conditions of an existing society.
That's what fundamentally separates the working class from the capitalist class. We can barely survive with the subsistence wages (crumbs, really) that the capitalist hand down to us, which is a tiny portion of the value produced by our labor.
Meanwhile, capitalists' entire existence AS capitalists presupposes the M-C-M' process. The extra value realized at the end of the process takes two forms - "Basic reproduction" - living expenses, luxuries, etc., and Capital reinvested in the business enterprise.
So now that we've covered the Labor Theory of Value in depth, let's move on.

Many who have only read Vol. 1 of Capital think (with good reason) that the "surplus-value" created in the course of production is what liberals call "profit", but that isn't the case. To be continued..
Before I move on, I want to make sure everyone understands the LTV using a concrete example (these numbers are totally made up and not realistic, I know, but bear with me)

Say a carpenter uses $20 of lumber to create a chair worth $500, over the course of 10 hours.
In this example, the carpenter has added (or, if you will, MADE) $480 of value in 10 hours. Let's assume the carpenter gets paid $15/hour. That means he's earned $150 over 10 hours. But has he MADE $15/hour? No. He's MADE $50/hour. He just only got paid for the first 3 hours.
The other 7 hours were him working for free, gratis, like an enslaved person. All of the value produced by his labor over those 7 hours goes into the pockets of people who didn't do the labor. Of course for this example I've assumed that the only costs of "constant capital" are
the lumber, which is an absurd assumption, but we have to simplify these things in order to have them apparent and easy to calculate. So when we Marxists say that capitalism is exploitative, we don't just mean that in a rhetorical sense. We can actually show you the MATH.
This leads me to the last point I forgot to mention about the LTV - the "rate of exploitation", or the "rate of surplus-value". We can literally calculate the extent at which each worker is exploited. Let's use the above example.
The carpenter's wages, or "variable capital" only make up $150 for the 10 hour day. The "surplus-value" produced by his labor amounts to $330 ($20 for constant capital + $150 for variable capital, subtracted from $500 - the value of the chair).
This can be expressed in this way - 20c+150v+330s=500V

You still with me?

To calculate the "rate of exploitation", you take the surplus-value and divide it by the variable capital (wages paid).

So in this example, it would be 330/150=2.2, or in other words, a 220% rate.
In Vol. 1 of Capital, Marx really only describes the process of PRODUCTION. He doesn't even begin to discuss DISTRIBUTION, or PROFIT as a whole. So for those who have read Vol. 1 but stopped there, this is where you need to really start paying attention:
In Vol. 2, Marx focuses on the process of distribution, or what he prefers to call "circulation" (like in a human body, our blood circulates - in an economy, Capital circulates in the same way. The heart of the economy is Capital, pumping that blood where it needs to go).
Marx explains how many factors go into the circulation process, which determine and affect how much of that surplus-value created in the course of production gets back to the capitalist in the form of Money Capital, and how quickly.
This includes how quickly goods are able to be transported to their market - and in his day, this was particularly important, since often the markets for the goods produced in colonial countries like England might take months to reach their market. To be continued...
This obviously creates some problems for the capitalist, because no capitalist wants to sit on a pile of Commodity Capital for too long before turning it into Money Capital, which he can then spend to support his lavish lifestyle, and reinvest in the business.
Marx also points out how some industries produce commodities which may take months or years to produce even one commodity - think of locomotive manufacturers, or steamship manufacturers in his day, or massive construction projects, etc.
To pay for the commodities being produced in these industries, capitalists must develop "hoards" of money from the revenue of each sale, in order to pay the workers their wages and pay for upkeep, raw materials, etc. in the meantime, before the, say, train can be built and sold.
This is where things get a little complicated. I've already covered the basic Labor Theory of Value, and its constituent components - M-C-M', in shorthand. Well what happens when capitalists in these types of industries (producing goods which may take months or yrs. to build)
invest a certain amount of Capital, and don't see a return on it for months or years? This is where the "hoards" of money become more important. Let's take an example. Instead of investing, say $1000 in a production/distribution process, and waiting a year for a return of $1500,
maybe the capitalist will only invest $800, leaving the other $200 in a hoard. That $800 will go into the production process, and begin the distribution process, while the other $200 is invested at some point during this process. The returns will come in unequally, at different
times, but this kind of practice allows capitalists to operate businesses like these and keep the wages and business expenses paid for, even when their commodities may take months or years to sell.
This FINALLY, brings me to the concept of "profit", which isn't even mentioned until Vol. 3. Contrary to what many Marxists think, surplus-value IS NOT PROFIT. It's an entirely separate entity, and has an entirely different equation.
The formula for profit is this:

Surplus-value / (Constant capital + Variable Capital), or

S/(C+V)

In other words, the difference is this: the rate of exploitation is only the ratio between the surplus-value created in the production process and the wages paid out.
PROFIT is the ratio between the surplus-value and ALL of the investment put into the production process, including constant AND variable capital.

So the "profit rate" will ALWAYS be a lower value than the "rate of exploitation", because there's an added cost in the denominator.
Profit is seen, from the perspective of the capitalist class, as the due compensation they deserve for providing the means of production, tools, wages, etc. needed for the entire production process to take place. Of course, it's circular logic -
Because they own something, they think it entitles them to owning something else, because they owned the first thing - nevermind that ALL the extra value produced in the course of production and distribution is produced by the workers, not them.
So at this point, we've covered the LTV, the rate of exploitation, and the rate of profit. A quick caveat here - Marx explains (and I have to admit, I haven't fully wrapped my mind around it yet) how the rate of profit is not just determined by the above equation -
rather, it's somewhat socially determined in each individual industry. The profit rate for an industry is the average value you get when you compare the profit rates of all the capitalists IN that industry. If an individual capitalist has a profit rate above or below that,
They are either at a competitive advantage, or a disadvantage. This leads to some conclusions which I won't touch on here because frankly, I haven't been able to understand them yet, and I'm hoping the David Harvey Companion will help me get there!
Now that we've covered all that ground, I want to start getting into Marx's central thesis: the tendency for the profit rate to fall. This is what I wanted to explain with this whole thread, but I thought it wouldn't make sense without providing the proper context.
So let's review a little first - the equation to determine the rate of profit is S/C+V.

Well as industrialization develops, and new, more efficient technologies are introduced to increase efficiency, this has some interesting effects.
1) As productivity increases, the price of each individual commodity produced decreases. Why? Because the time it takes to produce each commodity decreases. So why would a capitalist try to increase productivity, if they'll make less money from each commodity?
Well, the answer is obvious - they're able to produce a lot more commodities a lot more quickly than their competition, and, given that they're able to sell those commodities at the same rate, all other costs remaining the same, they will have a competitive advantage.
But what happens when new technology is introduced into one workplace which increases productivity? Over time, other businesses in the same industry begin to introduce those technologies themselves, or similar ones - at which case, the original capitalist loses their advantage.
But that original capitalist by this point has made so much more money than his competition, that he's able to increase the scale of his operations by injecting that Money Capital directly back into his business, opening up more factories, etc.
In the short term, again, this gives that capitalist a competitive advantage. But it's at this point where we start seeing something very interesting develop.

Remember the formula for determining the profit rate? S/C+V?
Well as businesses expand, and capital accumulation accelerates, what starts happening is that the ratio between the Capital spent on constant capital vs. variable capital begins to get all out of whack. More and more Capital needs tobe invested in constant capital vs. variable.
Unless it isn't obvious why this happens, I'll quickly explain - think of how much it costs for UPS to build a whole new commercial "hub" (it's in the millions, or tens of millions), and then to make it function. This requires buying tons of new trucks, (to be continued...)
conveyor belts, packing material, buying insurance, the depreciation on the trucks $ bldgs., hiring more janitors, engineers, mechanics, supervisors (remember, none of these jobs create more value for the company - their salaries are all factored into the "constant capital").
Of course, when they open up a new hub, they need to hire more preloaders, package sorters, drivers, (all of which DO add value to the finished service UPS provides - transportation). But the amount of variable capital (wages) paid to these productive workers is a tiny fraction
of the investment and continued expenses UPS has to put into not just building a new hub, but keeping it in operation.

So what you'll see over time, as capital accumulation develops in any one business or industry, the ratio between "constant capital" investment and
"variable capital" investment becomes more and more skewed. And since the equation for the rate of profit is S/C+V, as the costs for constant capital go up in proportion to variable capital, the profit rate falls. Let's use some made-up numbers for an example:
Surplus-value 10,000

constant capital 8,000

variable capital 2,000

So the "rate of exploitation" (again, S/V) is actually 500%(!!) in this case, which is extremely high, right?

But the "rate of profit" (again, S/C+V) is only 100%.
Let's compare that to an earlier point in the process of accumulation, where the ratio between constant and variable capital are less skewed.

surplus-value 10,000

constant capital 5,000

variable capital 5,000
The rate of exploitation would be 200%, but the rate of profit would be 100%. In the first example, the rate of exploitation was 500%, while the rate of profit was 100%. See how this works? The more constant capital invested vs. variable, the lower the rate of profit.
And this is an inevitable process which all capitalists have to follow, due to competition. If one business grows its operations in order to temporarily offset their lower rate of profit, other businesses in the same industry have to follow suit.
Now Marx addresses, in the same chapter detailing his central thesis, many different ways that capitalists find, in order to temporarily offset the tendency for the rate of profit to fall.
These include finding cheaper raw materials, paying workers less, working them longer hours, shortening the time between production and sale, expanding the business, using cheaper labor in poorer countries, etc.
The problem inherent to all of these methods is that, yes, they can temporarily increase the rate of profit - but when that happens, what is the inevitable result? More capital accumulation, which then has to be invested in more constant capital vs. variable capital,
which causes the profit rate to fall even further than before!! This process is a race to the bottom, and set the stage for what came shortly after Marx's death - the age of Imperialism, where these internal contradictions in each capitalist country reached a breaking point.
These industrialized countries were sitting on massive hoards of money which they couldn't put into productive use anymore, and more expansion was required. This led them to reach outside the borders of their countries, and try to dominate and exploit other countries.
This is what eventually led to WWI, and eventually WWII. Today, we've reached a new era - the era of neoliberalism, which began around 1980, and has become the prevailing doctrine of capitalist imperialism the world over. See, even imperialism has its limits -
There are only so many countries in the Global South to exploit, and only so many billions of people who can be ground into the dust in the Global South. So these imperialist countries have started turning inward again, in order, in a desperate, failed attempt, to again offset
the world-wide falling rate of profit. Austerity measures like the cutting of wages, pensions, job security, union rights, increases in tuition and rent and food costs, tax breaks for the rich but not the working class -
David Harvey calls neoliberalism "accumulation by dispossession". He compares it to what Marx termed "primitive accumulation", but flipped on its head - rather than enclosing the commons and forcing serfs off their lands and into the workforce(which is still happening elsewhere),
these imperialist countries have decided that their last chance to survive is to just destroy the working class's standard of living, and keep making it worse until there's nothing left - THIS is why capitalism is unsustainable, and exploitative.
I hope this has been understandable, and a good summary. I know it's been long, but I hope many of you have gotten through it all and have learned a lot. I will answer any and all questions anyone has. Thanks for reading!
And please RT this for me, I put a lot of effort into it and want this info getting out to as many comrades as possible! Most people aren't total nerds like me and will never make it to Volume 3 lmao. That's why I wrote this, to explain what they missed, which is CRUCIAL.
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