I believe in a minimum wage. Companies adapt to regulation in the same way that they adapt to market competition. If a community insists that companies have to pay at $7.50, a company has two choices: figure out how to create a profitable business even while paying this much or go out of business. A community has no obligation to keep in business a management team that can't figure out how to design a business to be profitable while paying people something approximating a living wage.
That said, there are at least two things that need to be considered in setting a minimum wage.
The first is the current distribution of wages. A third of Americans make an annual salary that equates to less than $10 an hour. Half make less than $15 an hour. If you - as Seattle has recently done - decide that the minimum wage should be $15 an hour, you have to explain yourself. I completely agree that laggards who can't, say, pay at least $7 an hour should be forced to change their business model or close shop. I like the idea of a legislative sheep dog nipping at the heels of the businesses that are in the bottom 10 to 30%, forcing them to move faster. It's a different thing, though, to suggest - as a $15 an hour wage does - that all the jobs should be above average. They won't be.
And that takes us to the next problem with the minimum wage. Whether it is set to $1 an hour or $25 an hour, there will be some people who aren't productive enough to cover that wage. It makes sense to tell businesses that they have to pay a certain minimum; regardless of what it is, though, some people are not productive enough to merit hiring. Those people need subsidies of some kind; not all needs will be addressed with a living wage.
The deeper need is for study of how jobs are evolving and a search for ways to move median productivity and wages. Individual success moves you from the bottom of a bell curve to the top; community success recognizes that there will always be one person at the bottom and one at the top of the distribution and will focus instead on moving the whole curve.