The Indiana House apparently voted to cap minimum wage yesterday, apparently so that local cities and counties cannot hinder business by requiring larger amounts. I don't know the specifics, so this is a theoretical exercise rather than a clear critique.
As usual, the ethical calculus involves two primary considerations: fundamental principles and consequences, with a check on motivations.
The fundamental principle behind a social contract such as the US Constitution is mutual benefit. The driving force behind the origins of capitalism was utilitarianism, the greatest good for the greatest number. Philosophically, we might call this cocktail: universal ethical egoism. Western systems aim at the greatest good for all individuals.
This amounts to a system that aims at the greatest good for the greatest number, with protections for the individual. I consider this the most fundamental principled framework for a secular society. By a happy correlation, it also fits well with the fundamental Christian value of loving one's neighbor.
The goal of social structure is thus not to make a few very rich at the expense of the majority. The best social structure is one that tends to result in as many people as prosperous as possible while protecting the individual from the prosperity of others, in fact aiming to empower every individual at least to self-subsistence. Again, this is the fundamental ethical value of the United States and Western society in general.
So given the goal, how does the minimum wage debate connect?
First, the goal in business--from the standpoint of societal structure--must be to prosper everyone in connection to that business as much as possible. This obviously is not the business owner but the employees and people who benefit from the business. Although it's easy to lose sight of it, this actually was the founding purpose of capitalism.
Capitalism holds that a system of competition will result in the greatest benefit both to buyer and seller. The buyer will seek out the lowest price and the seller will charge as high as they can. Ideally, they will meet in the middle with the most beneficial middle ground. But the goal of capitalism was not originally to make the owner of a business as rich as possible, which is why protections evolved for individuals like minimum wage and anti-trust laws.
Without those laws, capitalism had gone counter to its very founding purposes--mangling everyone it could in the service of the filthy rich. In my opinion, this is the trajectory we are on again, the Tea Party trajectory. We are now in the process of trying to peal back the protections of the individual, put in place at the end of the 1800s and beginning of the 1900s against capitalism gone amok. Unbridled capitalism does not accomplish its founding goals. This is the lesson of history. Only a moderately regulated capitalism does.
Minimum wage ensures that an individual worker can earn at least a subsistence level income. It would seem to be a fundamental value. Capitalism left alone will not evolve a fair wage because of the collusion of business. Places without minimum wages--Mexico, China--demonstrate the condition of their workers. Eventually, the global economy will evolve a world-wide minimum wage. We are in the throes of the transition, where American companies have temporarily shipped jobs elsewhere to get around the protections of the more evolved American system. But of course, that's an issue of union wages rather than minimum wage.
But it's not as simple as business versus worker. Low prices benefit the consumer, so the "greatest good for the greatest number" is not simply a calculus between business owner and employee. A thriving business benefits the broader economy. It benefits the people who buy the product in lower cost.
So the best minimum wage will be 1) one that reasonably allows an employee to live while 2) maximizing the benefit to consumers in the resultant prices and 3) does not demotivate the business owner from running the business. You can't put a precise number on these, unfortunately. The number changes from time to time and involves a significant element of cultural subjectivity.
But the last paragraph, in my opinion, is the ethical calculus for an optimal society.