Is minimum wages set by the government lead to unemployment?
Great question! That minimum wages laws cause a shortage of jobs is the sort of thing that people learn in Introduction to Economics when they first start learn how to recognize shortages and surpluses in economic models, but which isn't true at all. That happens a lot with beginner's economics, actually, because it's taught using a spot measure. Economics is dynamic, however, and j-curves are common. The j-curve is a graphed line that drops suddenly then increases past its starting point, making it look like a "j". The reverse j-curve does just the opposite. Minimum wage laws are an example of this. Yes, there is an instantaneous shortage, but as higher wages allows a wider consumer base to increase their spending, companies can charge higher prices to accommodate the increased costs of the minimum wage. This is called cost-push inflation. The reason demand for employment increases is because the increased income earned by a group of people who spend 99% of their income (they have a "very high marginal propensity to consume") is stimulates demand. In other words, almost every extra dollar earned generates business revenues, which will force companies to expand operations to keep up with demand. Of course, that's only helpful in a recession.
Another thing to consider is the influence on black-market labor. Hiring people "under the table", and no that's not just referring to illegal immigrants. There are a lot of people who do it as a tax-dodge. Increasing minimum wages increases demand for illegal labor. That's the thing with the vast majority of government economic regulations: they don't work. You can only influence an economy, not control it. Attempts to stop supply or demand through regulation only creates profits for those willing to break the law to meet equilibrium. Alcohol prohibition in America actually only succeeded in lowering consumption for 1 year, then it went up to normal levels. So, raising minimum wages in an attempt to raise total average wages will always be at a ratio of less than 1, making it highly inefficient.