(Also in the replies to one of the comments)

In Capital volume two there’s a section on the expanded form of capitalist reproduction and the simple form of capitalist reproduction. It’s basically how the capitalist system reproduces itself so it continues after a production cycle. It’s an analysis of the entire system, instead of just capital in isolation.

The entire economy can be abstracted into two departments.

Department I is the production of the means of production: all of the factories and private enterprises, etc. owned by capitalists that produce the means of production. The means of production are commodities like industrial machinery, mining equipment, smelters, tools, electrical infrastructure, chemical intermediates, Dow Chemical teflon coating, dyes, iron gear wheels, basic circuits, etc. Consumers don’t buy this stuff (unless they’re nerds), companies do.

Department II is the production of the means of consumption and the production of commodities for consumption: Coca Cola, Nestlé, Chiquita bananas, all of the companies you see in grocery stores, pharmaceuticals, coffee, personal use vehicles, personal computers, smartphones, fast food restaurants, avocados, diamond rings, private jets, etc. Department II is what consumers actually buy.

The value in departments one and two can both be expressed by:

c + v + s

c is constant capital, which is portion of capital that doesn’t grow, it’s value of the ingredients and the cost of maintaining the equipment that processes those ingredients.

v is variable capital, which is the same as “the total wages paid to workers.” It’s variable because it’s the portion of capital that actually grows, because labor-power is the only commodity that creates more value than its cost to purchase (wages).

s is the surplus value. Surplus value is the value produced by workers beyond what is needed to reproduce their labor-power. It’s the value produced during the unpaid part of the working day that capitalists are able to extract from workers because they own the means of production. It’s the profit.

Constant capital (c ) and labor-power (v) are being bought by capitalists to be turned into new commodities with surplus value (s) added to its value when it’s created (c + v + s). The new commodity is then sold for money and the money is used to pay wages and buy new constant capital for the next cycle of production.

Departments one and two must be balanced, because if they aren’t, then capitalists will find out that they can’t sell their goods because there’s not enough buyers (crisis of overproduction).

The first example of the meme is the simple form of reproduction. The simple form of reproduction is when the surplus value generated by the production process isn’t re-invested into expanding the production process and is entirely consumed by capitalists.

s = s_c + Δc + Δv

s_c is the portion of surplus value consumed by capitalists.

Δc is the portion of surplus value being used to buy additional constant capital, beyond just replacing the original, and Δv is the portion going to buy additional labor to expand a company’s workforce.

In simple reproduction s=s_c and Δc and Δv both equal zero. So in the first example the capitalists are spending all of their profit on like gold steaks, or ballrooms, or sculptures of balloon animals, or whatever.

For it to balance Department I must replace its own constant capital, so… c₁ + v₁ + s₁ - c₁ = v₁ + s₁

This is like the stuff that goes into producing the stuff that produces the means of production.

Department II must produce the means of subsistence for its own workers and in this scenario, its capitalists are spending all of their profit on each others Dept.II companies… so c₂ + v₂ + s₂ - v₂ - s₂ = c₂ = c₂ All that’s left is c₂ and Department II must buy this constant capital from Department I.

And Department I must also produce the constant capital used by Department II, so…

v₁ + s₁ (the remaining value in Dept.I after it has renewed its own constant capital) must equal c₂ (the constant capital that Dept.II requires).

v₁ + s₁ = c₂ (The balanced equation for simple reproduction.)

This is stable, but we rarely see situations like this in reality.

In expanded reproduction there are the same two equations for the value of both departments:

(Dept.I) c₁ + v₁ + s₁

(Dept.II) c₂ + v₂ + s₂

I already gave an explanation for what those variables mean so I’ll skip over to the different bits.

In expanded reproduction s != s_c and Δc and Δv for both departments are non-zero (in real life the vast majority of profit gets re-invested as there’s just no way the bourgeoisie can spend billions on consumer goods every year, nobody could ever use that much money). s = s_c + Δc + Δv so substitute it in where s was.

The full equations look like this now:

(Dept.I) c₁ + v₁ + (s_c1 + Δc₁ + Δv₁)

(Dept.II) c₂ + v₂ + (s_c2 + Δc₂ + Δv₂)

To balance them now we require that Department I renew its constant capital, so you just substract c₁, but it also must renew its newly bought constant capital, so substract Δc₁ too:

(Dept.I) v₁ + s_c1 + Δv₁ (The value left that is able to circulate out of Dept.I)

Do the side but since Department II produces its own labor-power it’s s_c2, v₂, and Δv₂ that cancels so it gives you:

(Dept.II) c₂ + Δc₂ (Constant capital needs to be bought from Dept.I)

This must be able to renew Department II’s constant capital (and newly bought constant capital) so the balanced form of expanded reproduction is…

(Dept.I) v₁ + s_c1 + Δv₁ = c₂ + Δc₂ (Dept.II)

However, as you can probably see, this requires the growth of Department I to be in lockstep with the growth of Department II or else commodities are being created that nobody can actually afford. Capitalism has no way of balancing these departments, they act independently out of self-interest.

Department I can buy from itself like a feedback loop and then realize its in trouble once its producing too much for Department II to feasibly buy, but the capitalists can’t stop themselves, because once the crisis hits, if they didn’t grow then they’ll go under! This can only be resolved by Department II growing beyond capacity as well, or by sections of Department I going bankrupt.

Department II are all competing for the consumer’s attention, all at once. And all of those companies are trying to grow, all at once, but the total wages of workers plus the amount spent by capitalists can’t consume all of it.

Almost always:

(Dept.I) v₁ + s_c1 + Δv₁ ≠ c₂ + Δc₂ (Dept.II)

So there are cyclical crises overproduction where huge swathes of capital that has over-accumulated devalues or is destroyed, and afterwards there is usually even more inequality, and the economy is more monopolized and more financialized, so the next crisis will be even bigger.