Note: This article does not include any "capitalism is good/communism is bad" aphorisms and it is not intended for any political discussions. What follows is merely an economic exposition.
When the name of Karl Marx enters a conversation, our minds spring to themes of collective societies, USSR-style governments and hard-headed dictators. What we seldom remember though is that Karl Marx was an economist and one of his most famous contributions (and the one on which he based the Communist Manifesto) was his, interpretation and expansion of the thoughts of David Ricardo and Adam Smith on the Labour Theory of Value.
Quoting another blogger, the labour theory of value simply states that "... the "value" of a commodity is determined by the "socially necessary labour time" embodied in it ("socially necessary" to avoid the nonsensical idea that somebody who makes something slowly will contribute more value than somebody who makes the same thing, but faster)." It should be noted here, that this theory has never been a theory of prices as (under Marx's explanation) even though prices might fluctuate, the overall value in the economy will remain the same. Deriving from this, Marx expounded the notion of the "tendency of the rate of profit to fall", again building on the work of previous economists, who noticed that the rate of return of capital invested in industrial production declined over time.
Marx concluded that in order for the rate of profit to continue to be as high as before, "capitalists" had to employ other approaches, notably to exploit the labour force under their employment. This, in Marx's opinion, led to frequent crises in the capitalist system, which were caused by labourer's revolting against the low wages brought on by employers who tried to earn more.
As already stated two paragraphs ago, what makes a product more valuable is the "socially necessary labour time" embodied in it. This simply means that the reason why air conditioners are more expensive than simple pens is that it takes longer to manufacture them. I doubt anyone could actually disagree with that; yet, what is more interesting is what comes next. In order to see where the exploitation of labour comes in, we have to distinguish between two points of view: one where the labourer is his own master and whatever he produces he can sell and another where the labourer is an employee. If what the labourer can possibly earn in the first case can be more than the amount earned in the second, the we can say that we have exploitation.
Let's start with the following scenario: average Joe can produce X amount of good G, with an estimated value of V (notice we are not talking about prices here). This amount is what Joe is contributing to the economy. Now suppose that capitalist C offers Joe the following plan: he will work the same time as before and earn the same amount of income, but the capitalist will offer Joe some capital (think of it as a machine assisting in the creation of good G), and Joe will be expected to produce amount Y (Y>X). The difference between Y and X, multiplied by the price, is the capitalist's profit (we will consider that the rate of capital here is constant*).
Given that Joe's job is rather unstable (just like any other self-employed person in the world he does not know whether he will be able to sell all the goods he manufactures), having a stable income is much more preferable (the fact that his wage will be the same as before means that he is not losing any purchasing power). Now, since less effort than before is given into making the same amount of goods, according to the labour theory of value, the value of a unit of good would decline. Yet, would the overall value of goods also decline? The answer here is that it depends: if Y*V2>X*V1 (with V1 indicating the original value and V2 the value after the capitalist offered some capital) then it would not. Thus, if the increase in amount of production, induced by the addition of capital multiplied by the new (reduced) individual value is greater than the original then the economy is better off than before.
Why should the capitalist care about increasing value in the economy one might ask. The simple answer is because it increases his profit. His profit is Y*V2-W (with W being the wage he pays Joe), meaning that the higher the value, the higher his profits, given that Joe's wages are constant. This is simply increased return on labour and not on capital (we considered that to be constant before). How would the capitalist, in real life, know that it is good to perform that action: simply, trial and error. If the price more than expected and he cannot make a profit then he just shuts things down, or reduces wages.
Obviously, the rate of return on capital cannot be same, not through time and neither through sectors. For example, the rate of return was huge in the DVD rental industry in the early 2000's, and has taken a nosedive since. Yet, it had nothing to do with labour nor capital. It had everything to do with shifting preferences (from DVDs to pirated movies or Video on Demand). In addition, diminishing returns also imply that adding more and more capital cannot really help you to increase your rate of profit; most of the time they actually decrease it.
Returning to our discussion, Marx was right: wages might fall and capitalists do earn of what their employees produce. Yet, Marx was wrong on that capitalists have to make misers off their employees to earn a constant rate of return (we, of course, do not argue that regulation is very useful in protecting some form of worker exploitation): they just have to find new ways of being more productive or, even better, generating more demand for their goods.
The falling rate of profit actually has a meaning of its own: it shows you whether people are actually enjoying your product or if you are going to have a full-blown disaster. If we consider the falling rate of profit then we have to define what it stands for: just commenting that it falls means nothing. It falls either because you are doing something wrong or because you are obsolete. In either case, shutting down a business is much preferable to continuing its operation just for the sake of keeping some people employed at a lower wage. It is also better for the employees, even though earnings new skills to keep them marketable may be hard.
*A little bit of math: A production function of the Y=K^(1-a) means that we have constant returns to capital of the rate r=(1-a)*K^(-a). Then, if we add labour, we have the Y=L^a*K^(1-a) form, meaning that we add a*L^(a-1) return to the previous, without the return from capital changing. What the capitalist offers is a wage equal to the marginal product of labour, i.e. w=a*L^(a-1). Yet, if the worker's earnings from before were less than w, then the capitalist can profit from that as well.