It's hard to trace products through the entire chain of production, but yes, in Sweden it's quite hard to buy products and services produced without the union setting the wages (there are no minimum wages set by law, only unions, and the union negotiates wages also for non-union employees). It might be under the headline "Scandinavian model" of that econ textbook.
Ah, sorry to knock your country of residence, perhaps unions work differently in Sweden. In the USA, unions use their monopoly power to push wages above the competitive rate, at the expense of consumers, the unemployed, and nonunion workers. Imagine if you were looking for your first job, and you were only allowed to be employed at union rates. It would not be easy to convince an employer to hire you. Perhaps that's why so many youth in Sweden are unemployed?
Also, in the US, I have the freedom to negotiate my own wages, rather than having them negotiated for me by a union over which I have no control. This means that if I work harder or smarter I will earn more. Personally, I like having control over my own destiny in this way, and society at large reaps the benefits of more motivated and productive workers.
If wages were left to market mechanisms, there would be no need for a set minimum wage. The fact that there is a minimum wage, and that many earn just that, is a clear indication that the market price of labor isn't negotiated between parties of equal strength.
To be clear: regardless of who sets the minimum wage, there is a minimum wage, and you aren't free to take a job under that level. To be honest, it would seem easier to "control" the union of which you are a member, than to adjust the minimum wage. It's just two organizations where one (congress/parliament) feels larger and further away.
A huge drawback of a single minimum wage (not differing between different parts of the labor market) is that it will spel trouble for companies when businesses on different parts of the cycle would be treated the same.
As an example, here companies relying on export such as truck makers are hugely sensitive to drops in global economy, and unions will accept frozen wages to limit layoffs as soon as bad times hit, which it does early in the cycle. Meanwhile service jobs or the public sector may be at a completely different point in the economy cycle, with perhaps 1-2 years before bad times hit. To use the same wages in both parts of the labor market would be a rather blunt solution.
I agree with you that a minimum wage can be beneficial in industries where wages are not negotiated between parties of equal strength, for example, the giant Walmart that employs half the people in town. In this case, economic models show that a minimum wage could actually increase employment by pushing wages closer to what the competitive wage would be.
However, I'd argue that in many (if not most) industries this is not the case. In fast-food and software, for example, the workers are free to move between employers at will, giving the workers significant power to negotiate.
I remain skeptical that governments (or unions) are smart enough to set the correct minimum wage without going under or overboard, which would hurt the unemployed and consumers. A better solution, I think, is a basic income system that ensures nobody is in poverty. http://en.wikipedia.org/wiki/Basic_income
“We rarely hear, it has been said, of the combinations of masters, though frequently of those of workmen. But whoever imagines, upon this account, that masters rarely combine, is as ignorant of the world as of the subject. Masters are always and everywhere in a sort of tacit, but constant and uniform, combination, not to raise the wages of labour above their actual rate…Masters, too, sometimes enter into particular combinations to sink the wages of labour even below this rate. These are always conducted with the utmost silence and secrecy till the moment of execution; and when the workmen yield, as they sometimes do without resistance, though severely felt by them, they are never heard of by other people” In contrast, when workers combine, “the masters..never cease to call aloud for the assistance of the civil magistrate, and the rigorous execution of those laws which have been enacted with so much severity against the combination of servants, labourers, and journeymen.” - A Wealth of Nations