Yep pretty much.

Also the first capitalist to find a lower-cost way to produce, like with automation, gets a disproportionate share of profits at first and can even use it as an opportunity to gain overall marketshare, thus increasing their bulk of profit even if per-unit profit has decreased. For example, if they sell a table for 25% less due to cutting labor costs by 30% but sell 50% more of them, their total mass of profit has increased (albeit temporarily unless they have a monopoly).

It's about comparative advantage in the short term as well as the tension between labor and capital. Not to mention the natural proclivity for people (mostly workers) to improve processes they are involved with, improvements that are usually claimed by the capitalists and incorporated into the capital mass. Whether the improvements are actually incorporated or secreted away and suppressed, though, depends on the former points imo.

Comparative advantage is one capitalist's ability to outproduce others, beating them to market or enjoying higher margins, ultimately hoping to monopolize. Socially-necessary labor doesn't adjust instantaneously, it shifts according to the degree a given technology is commonly accessible or in proportion to the amount of the commodity in that society is produced with said technology versus older technologies.

The tension or contradiction between labor and capital here is that labor has a fundamental power in the dialectic, inasmuch as labor's contribution to the system is the one that "matters"; capital's power in the relationship is arbitrary or enforced (a sort of lord-bondsman dialectic). The very definition of capitalist necessitates an exploited worker, but not vise versa. Thus capital is always looking for ways to subvert labor's power. Automation and the threat thereof has a localized effect of temporarily disciplining labor.

Without competition and/or tension from labor, I don't think there's much impetus for capitalists to improve upon their systems. Labor is comparatively cheap when disciplined.

At least that's how I understand it.

This is the subject of Part Four: The Production of Relative Surplus Value.

But to jump ahead, imagine a global village where 10 capitalists all produce yarn (buying labour power and means of production in market etc). We will hold the length of the working day steady (as this is the end result of chapter 10).

Each capitalist produces 10 yarn in a day, each bearing 1 unit of value, and hence each capitalist, after selling their yarn, has 10 units of value. The working day cannot be increased, so other methods of increasing the portion of the working day devoted to the production of surplus value must be found.

Suddenly one of the capitalists finds a way to increase the productivity of his spinner, whether by some new machine or by some new organizational method. This capitalist can now produce twice as much yarn in a day per unit of labour power. Hence, he produces 20 yarn a day with the same amount of variable capital. If this new method of production were adopted generally, socially necessary labour time to produce yarn would fall by half, each yarn bearing half as much value. Consequently, if this new method of production were adopted generally, this capitalist would find no new profit, as you say.

But the other 9 capitalists are still using the old production methods, because of patents, lack of funds, etc. Hence, the socially average labour time to produce the yarn hasn't fallen by half; it has fallen by 5% (unless my math is wrong; regardless the socially average labour time falls slower for society than for the capitalist using new production methods).

Each of the other 9 capitalists continue producing as they had before, but now their day's product of 10 yarn bears only 9.5 units of value, in spite of their workers continuing to work for as long as they had before. They begin to see a deficit. In contrast, the capitalist using new productive methods has produced 20 yarn bearing 19 units of value.

This is one of the contradictions that becomes an issue later. Profit is highest when variable capital is highest, but you are not producing nearly as much. The speed at which you produce also affects profit. You then enter an overproduction crisis, when you have less people paid well enough to consume, but capitalists have an overabundance of products, they can no longer sell.

While labour-intensive production might be more profitable for the bourgeois class as a whole, individual capitalists don't really have a choice in the matter: they have to use the most efficient process available to compete. Is that the Marxist explanation?

Yes. The bourgeoisie may be a class with a common interest as capitalists but that does not mean there is not struggle within the bourgeoisie. An individual firm that wants to survive, let alone surpass the social average, must keep up with the state of the art, or perish.

In those industries which have absolute monopoly due to legal mandate, you do see a plateau in technological development; everyone knows this from experience.

Even without competition there is still the possibility to increase profits by improving technology, thereby reducing unit value, while enjoying a static market price due to legal mandate or artificially limiting supply.

Your question is 100% valid and it strikes at the heart of the matter. Capitalists seek surplus value in whatever way they can find it. In certain economic conditions such as tense competition or strong labor, the capitalist might find they can only extract surplus value by producing commodities with less than socially average labor time by advancing technology. This is relative surplus value since the surplus value is relative to the rest of the book producers. But capitalists don't necessarily do this if absolute surplus value can be extracted. (Analysis of imperialism can be expanded here.)

While labour-intensive production might be more profitable for the bourgeois class as a whole, individual capitalists don't really have a choice in the matter: they have to use the most efficient process available to compete.

Yes, and this is part of a general contradiction that capitalism constantly reduces socially necessary labor to an absolute minimum, which at the same time disintegrates the basis of capitalism. (By basis I mean the extraction of surplus labor, the labor cannot be extracted if there is not a necessary labor to speak of.) Pre-empting some later parts of the book and also Volume 3.

CC is a multiplier for capitalist, if your shit machine makes 10 coats per worker and new shiny machine makes 12 coats per worker, your eyes lit up and you want new machine. You pay your workers the same and get more coats.

But uh huh new shine machine slowly propagates through the economy, and the amount of coats needed remains largely the same ( you ahve not changed worker compensation for them to buy more coats). Now you've done fucked up, and you fire some workers until new equilibrium is found.

if profit comes from exploiting labour-power, would capitalists improve technology?

Improved Tech makes the labor produce more value. If they exploit the same amount of labor and the labor makes more value they make more profits. If a new tech costs more to implement than the increased value of the labor it will not be implemented.

then the socially-necessary labour-time to make a book falls across the world.

The word "necessary" is really important here. It isn't "average" labor time.

If a factory with the tech doodad can make twice the books with the same labor and materials they will buy enough doodads to make all the books and lower the price of a book so the old style factories will be unable to make any profit and will thus close. Once the old style is gone they can slowly increase prices again until some new doodad is invented. All the book makers are trying to invent the next do dad so they can put competitors under and avoid going under themselves.