In the United States, there's talk of imposing a $10.10/hr national minimum wage policy (the vote failed). In some regions of the country, we've seen a $15/hr minimum wage established. However, there's still much conflict as to what the consequences of having a minimum wage policy are. Some people (particularly modern-day liberals and progressives) claim that not only does a minimum wage raise wages, but it also reduces unemployment by increasing demand. Others (usually libertarians and conservatives) claim that a minimum wage reduces employment by increasing costs to employers. I, on the other hand, think it's absurd to apply a single (and politically comforting) narrative to every single scenario wherein a minimum wage policy is imposed.
The impacts of a minimum wage policy will obviously depend on the location, the type of industry, the type of economy, the supply side structure of the economy, and a whole host of factors. Also keep in mind that a sensible minimum wage policy must take into account things like the cost of living, which varies heavily from state to state.
It seems obvious to say that states with different costs of living and states with different societal pressures and geographies need different minimum wage policies, but many arguments don't take that into account. For example, a state with a high youth population will need a much lower minimum wage than a state with an aging population. Another example of different states needing different minimum wage policies would be a state like Texas as opposed to a state like California. California has a very high cost of living along with one of the highest energy costs in the entire US. Since California has such a high cost of living, a $15/hr minimum wage may actually not be all that much in California. However, Texas has a very low cost of living where $15/hr would be absolutely insane. The imposition of a $15/hr minimum wage in Texas would certainly create all sorts of problems.
However, one of the most important factors in determining the suitability of a universal minimum wage policy among a locality, state, or country could end up being the supply side structure of the economy. If you were to have lots of capital intensive industries, raising minimum wages sharply will not have much of an impact on the company's balance sheet and may actually help businesses by increasing demand in the region. However, if the businesses in the region are very labor intensive, raising the minimum wage would obviously have much more disastrous consequences on employment.
Basically, all I'm saying is that there is no universal impact of a minimum wage on any sort of business, locality, state, or even country. Any sort of claim otherwise would easily be falsifiable. It depends on a host of factors including balance sheet structures, social structures, the supply side of the economy, along with others. In other words, having a non-existent minimum wage throughout every part of the country makes as little sense as having a universal $10/hr minimum wage throughout the entire country.
The best policy would be to have different minimum wages set by state and local governments differently. In some areas, a very high minimum wage actually makes sense while even a low minimum wage in other states could end up being very destructive. The only policy that doesn't make sense is a national minimum wage policy.