Marx's argument in the theory of exploitation is that capitalists do not need to sell their labour power in the market in order to live, whereas workers need to do so. As such, workers are not really "freely and voluntarily" participating in the labour market. This power differentiation enables the capitalists to exploit the worker, extracting surplus value from the latter.
This is one level, and a superficial one, of Marx's argument. But why would capitalists want to exploit workers, extracting surplus value from them? That's not just because they are evil or greedy; they are compelled to do that by competition; if they do not exploit the labourers, competition throws them out of the market, and ultimately reduces them to labourers themselves.
Yet, if a (sufficiently generous) universal basic income (UBI) were to
be implemented in a given country, workers would not need to offer
their labour in the market. Anyone who does so, would do it freely and
voluntarily. This not only eliminates the "slavery" side of the
argument but it might also reduce (albeit not eliminate) the level of
surplus value extracted to the worker (because, essentially, is giving
more power to the latter). Therefore, any "exploitation" in such
context is entirely agreed by the worker when entering a work
This doesn't eliminate the "slavery" aspect of the issue, because the decisions about the management of companies would still belong to the capitalists. The worker might in this case decide to not join a given company; but he will have no say on what the company produces, how it organises its production, etc.
To really make an effect, the UBI would have to be quite close to the share of each worker in the overall production. That would squeeze profits, and make the continuing of capitalist production impossible; most likely, capitalists would politically react and compel the State to repeal the legislation; if not, the system would crumble, either to be replaced by a socialist system, or into economic disorder.
Is this correct? Is exploitation no longer exploitation when no coercion is involved in the transaction? Would then UBI be such a "solution" to exploitation?
No. More likely, the result is just some diminishment of exploitation, that doesn't really change the system. If the UBI is pushed too high, it would put the system into crisis.
There is a more complicated discussion. In a capitalist society, value is the social form of wealth. But wealth and value are different things, which are not interchangeable, and their relation is, in Marxist terms, contradictory.
You can put things in these contrasting terms:
Two pairs of shoes are twice the wealth as one pair of shoes - and also twice the value.
When productivity changes, so that you can now produce two pair of shoes at the expense of the same amount of labour that you previously needed to produce just one, you double the wealth, but the value remains (macroeconomically) the same.
If you pay workers a UBI, unrelated to their labour output, you are assigning them a given part of the total amount of wealth produced - but you are also assigning them a part of the total value. While capital will have no necessary problems with the redistribution of wealth, it cannot deal with the redistribution of value: while wealth is increasingly abundant, value is not, unless labourers work more (or more labourers work). Indeed, in the conditions of capitalist production, value is increasingly scarce, and giving it away for free will create problems for the reproduction of the system, because capital needs to control a considerable part of the produced value, in order to reproduce itself.
So, beyond a certain level, even if there was absolutely no effect in the incentive to work (which is in itself a dubious assumption), the result of a UBI will be a crisis in the system, probably giving way to a backlash in exploitation.