Raising the minimum wage in the U.S. won't have any impact on the particular circumstance you mention. The problem of offshoring software development will continue. Somethings can't be off shored, of course. or can't be at competitive quality , but software is probably not one of those. Germany has been able to keep wages up and compete in manufacturing through superior engineering and design. Per capita they have a very high number of engineers, higher than in the U.S. for example. I think the answer, certainly the long term answer, is not to place artificial barriers, but to do the things that you can do better than anyone else. We could compete with Germany, for example, if we had a mind to but that would require better education of our citizens.
I see public education in the U.S. as a disaster, but not uniformly so. In some places, much of the Midwestern and Western states, it is good to excellent. Our failures are not because we can't do a good job, but because in places where we are failing we finance education with bake sales and highways with appropriations. [to some extent that reflects national priorities as well. Consider for example that the appropriation for the National Endowment for the Arts could be increased five fold by building one less F-35 fighter plane per year (the Pentagon has ordered 2,500 planes!)] To solve these problems we have created, priorities must change. Look at what States like Mississippi are doing with regard to public education and you will see a perfect model of what not to do. Mississippi seems to have perfected bad decision making and this aligns perfectly as well with the State's bottom ranking in level of poverty, teen pregnancies, educational achievement, and on and on. On the other hand, Kentucky is a State with a similarly large a indigent, rural population. Kentucky did the opposite of what Mississippi is doing with quite dramatic results.*
What is at the root of these bad decisions. Clearly it is ideology. And at the root of regressive ideologies is poor education, or lack of it. One malady feeds on the other and results in a downward spiral until there is intervention from the outside and a change in priorities.
When wages are too low not only does the wage earner suffer from poverty but the children of that wage earner are impacted as well! The first step in breaking out is recognition of root causes of these maladies and what is feeding them. Your post tells me that you are every bit as capable of recognizing these maladies and the root causes as I am. Raising the minimum wage is a necessary step in the right direction, but it won't be nearly enough.
We can't afford to do nothing and simply wait until the wages in developing countries rise to meet our falling wages [the minimum U.S. wage in 2016 is 31% lower than it was in 1965, and it is not just the minimum wage that has been falling, wages across the board in the lower half of the middle class have been falling since 1965.].
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*Not, of course, the result of their States legislative initiative on their own. They aren't a good deal more competent than Mississippi's ignorant legislature and Governor. But because the courts forced the legislators to change their priorities.