Others have already explained the meaning of those terms and I suggest also reading the sections of Capital that deal with those terms, which would be Volume 1 Chapter 8 for variable and constant capital and Volume 3 Part 3 for the TRPF, though the latter one is much more confusing and even somewhat controversial.

I guess I'll give a shot at explaining it in broad strokes: Suppose you have labourers (variable capital) and machines/tools/property necessary for production (constant capital) in order to produce commodities with a certain value attributed to it by both the labour used to make it and the labour necessary for the construction and maintenance of the constant capital. Labour is the key component because workers already exist prior to the production and seek to continue existing, requiring things like food and shelter in order to survive. They rent out their labour-time in exchange for money which is in turn exchanged for socially produced goods, meaning that this labour-time is the non-capital portion of the value of a product.

The capitalist will extract surplus value from that process, which needs to be reinvested. Both constant and variable capital grow. Broadly speaking, given growth in both variable and constant capital with a constant rate of exploitation (value minus wages) the proportion of surplus value extracted from value produced will decrease.

What your colleague seems to be pointing at is the reduction of the labour-time required for production of goods. An increase in production through better means (machinery, technology, techniques) that enable workers to produce more with the same amount of labour time will, in fact, lower the relative value of the given product (which in capitalist terms actually "increases" the value of that labour). The value itself is given both by the labour-time and capital upkeep (which can also be measured in labour-time i.e. Integrated Labour Cost). This is close to the TPRF but not necessarily the same thing.

I wrote a whole thing, but I think I can sum most of my argument up with a philosophical question. "If nobody made something, who are you paying for it?"

The hypothetical scenario where machine "labour" is cheaper to produce and maintain, and equivalent if not better than human labour crashes against the premise of labour theory of value.

At some point of the production process, either a living, breathing and eating human produced the machine or produced some part of the process for the construction of that machine. Those proletarians need to continue existing in order to work, which has a cost associated with it. Supposing a sector of the economy can be handled autonomously with those machines, their cost will have been the necessary cost of the (human) labour necessary to produce that automation or that provide the inputs for it.

This will mean that that industry will produce little-to-no relative "value" in a Marxist sense, and the cost-price will be determined mainly by external factors such as scarcity or abundance of the production for other areas of the economy, as well as political decisions (i.e refusing to lower prices). Prices can be kept arbitrarily high and wages arbitrarily low, the relative difference of which creating more surplus for the capitalist.

Supposing that the entire economy is maintained solely by machines, and that this automation is so total that not a single part of the process has human input, including maintenance, electricity and all sorts of other "externalities" handled by workers, then whatever is produced has no labour value.

This presents a problem for Marxist analysis, as this presupposes a completely unprecedented world where production no longer necessitates labour. In such a world, the exploiting class would have no need for an exploited class. Whether either class would be liquidated through violence or abolition of class distinctions depends on the specifics of this hypothetical. The answers for this aren't in the TPRF, but in the historical process of the formation of such a world.

Although I don't believe such a level of automation will exist in our lifetimes, I predict that the trajectory will remain the same as now, ignoring the possibility of revolution.

Current lucrative sectors of the economy will face desperate pushes for automation (entertainment and services in general with chatGPT and MidJourney, warfare with autonomous drones, etc) and as professions are turned obsolete by machines, workers will be laid off and redirected to more peripheral regions of the economy (food delivery). As those peripheral markets become more consolidated and lucrative, there'll be a push to automate those too.

At every step, labour will be marginalised and fractured by automation, only to be consolidated in whatever future equivalent of call centres are created, and then automated out of work again. Labour-time will become individually more productive and therefore relatively less valuable. There's no reason why capitalists of specific sectors would avoid automating it, as they'd get increases in surplus (assuming constant pay for infinitely more productive workers). And workers would be correct in demanding lower prices as automation decreases value, though monopoly capital would exercise its desire to maintain arbitrabily high prices.

So class society would become increasingly unstable as the economy gets automated in its totality, exacerbating the already existing tensions over the disparity of prices and wages and value and labour-time. On the capitalist side this could develop into pushes for diminishingly meaningful jobs on the periphery or even into violent "population control", and on the proletarian side this could develop into demand for higher pay and lower prices or the redirection the new surplus into public services, or the good old revolution.

https://cosmonautmag.com/2021/10/why-machines-dont-create-value/

For anyone who hasn't read this article, I think it brings together most of the important points to consider when discussing automation from a Marxist perspective.

I assume from your phrasing you mean to say that "some industrialists will prefer human labour over cheaper machines". (But you could instead have meant to say that "in society, there will always be a role for human labour").

I think this proposition is false (in the long run) due to the the profit-maximization logic of capitalism. Even if some industrialists prefer human labour, in the long run they'd eventually be out-competed by those that didn't. But yes, machines cost a lot upfront which could delay the switchover (possibly even beyond the sunset of the industry!).

I think the "Rate of profit falls" theory doesn't matter. Assume it's true: machines lower the rate of profit. But, capitalists can't (as a group) decide not to use machines. Without control of private assets (e.g. capital) the capitalists cease to be, and become a purely rentier class again. It would no longer be capitalism but feudalism. I don't believe capitalists have the power (or desire) to cause such a transition.

well capitalists still need humans because:

raw materials have to be transported by someone who knows where it's heading

someone has to do maintenance to the machines

someone has to sell the products

someone has to deliver the products

and all of that requieres human labor, and that's where the value comes, because the capitalist doesn't do any of those things

I am not the most well read on Marx, but from what I could understand from his discussion on constant and variable capital, the former still requires human work for creating, operating and maintaining it.

Machinery would only be deployed if it was cheaper than the human workers executing the same tasks, and its adoption would lead to layoffs, thus to the reserve army of labor, humans made "cheaper" by competing against the machines.

I am not acquainted enough with the TRPF to comment on it, but my assumption would be that once labor is made cheap enough the capitalists would not have any incentive to keep investing in automation, thus restarting the cycle. I have a vague feeling that the TRPF also mentions the impact on profits of a much impoverished consumer base (the laid off workers) , but I defer to any comrade who can correct my understanding

context might help; where does it come from?