Wages and their effects are a very complicated system. Note one key aspect of it however: a raise in wages by a company has a much smaller effect on the cost to provide a product/service than it has on the spending power of the people getting the wage increase. A business that increases it's wages by 10 % would see total costs increase more like 2 to 5 %. The wage increase being caused by a minimum wage would mean no change in competitiveness assuming each company passes the cost along to consumers, and consumers see a trivial increase in cost of living overall. Meanwhile those who got the wage increase see a significant increase in their spending power and standard of living.
A five percent increase in operating cost is the difference between solvent, and not solvent, for many small businesses. Minimum wage laws are CHOKING them to death. Minimum wage laws do more to help corporations kill their business rivals, then it does to help either the workers for those corporations, or their customers. I wonder what the numbers would look like if you compared the number of small business to big business ratios, from the start of minimum wages, to now, per capita. Be interesting.
There is a limit beyond which a minimum wage does more harm than good, and increasing the minimum wage does cause other issues. You cannot legislate away the "working poor". It will not work. Not surprisingly the pros and cons of a minimum wage and an increase to such tend to be overinflated by those for or against it. And that is where we reach the problem with your idea. First and primarily, it is trying to fix something that isn't broken. Minimum wages work and as long as increases are kept modest and spread out in time, increases do not have a significant negative impact on the economy.
A minimum wage always does more harm than good, it's just that the harm isn't seen till later. And no, you can't legislate away the working poor, but you CAN prevent the birth and growth of monopolies via legislation. True, minimum wages don't have a significant NEGATIVE impact on the economy...but also true, they don't have a POSITIVE effect, either on the economy, or for the people stuck earning such a wage. The secret to economic mobility, on an individual basis, is market volatility, in my opinion. A business was never meant to outlive, by generations, it's founder and original owner. It's like being a cashier at a store, wanting to promote to a front line manager, waiting for the current front line manager to retire...but said manager never gets older, never retires.
Secondly, an increase in the cost of living(inflation) is not a bad thing, and it is going to happen. Where it is a problem is when that increase is too high. Increases in the cost of living and related wage increases through market pressure have such positive effects as reducing the longterm cost of borrowing money as an example.
The direct result of minimum wage increases, increase in the cost of living. Not too bad a thing for those on minimum wages, and not really too bad for the wealthy. Not so great for all the folks in the middle.
Lastly, the more controls you try and place on a market, the harder it is for that market to self correct. That is the real highwire act, adding enough regulation on the market to reduce catastrophic or major failures such as recession/depression, hyper-inflation, etc, while not adding too much. You want to ensure that any potential good outweighs the risks, and in this case, your idea fails that test.
This is delicious coming from a self described "very liberal". What are the risks of requiring a maximum wage concept upon the major conglomerate business that call this country home? You've listed none, thus far.