In theory, there should be no need for a minimum wage, as employers should all be conscious of their grave responsibilities to their employees and provide wages which are sufficient to support them and their families. As Leo XIII says in Rerum Novarum
"Let the working man and the employer make free agreements, and in particular let them agree freely as to the wages; nevertheless, there underlies a dictate of natural justice more imperious and ancient than any bargain between man and man, namely, that wages ought not to be insufficient to support a frugal and well-behaved wage-earner. If through necessity or fear of a worse evil the workman accept harder conditions because an employer or contractor will afford him no better, he is made the victim of force and injustice."
And again,
"If a workman's wages be sufficient to enable him comfortably to support himself, his wife, and his children, he will find it easy, if he be a sensible man, to practice thrift, and he will not fail, by cutting down expenses, to put by some little savings and thus secure a modest source of income.Nature itself would urge him to this. We have seen that this great labour question cannot be solved save by assuming as a principle that private ownership must be held sacred and inviolable. The law, therefore, should favour ownership, and its policy should be to induce as many as possible of the people to become owners."
Later, Pius XI says in Quadragesimo Anno
"In the first place, the worker must be paid a wage sufficient to support him and his family"
"In determining the amount of the wage, the condition of a business and of the one carrying it on must also be taken into account; for it would be unjust to demand excessive wages which a business cannot stand without its ruin and consequent calamity to the workers. If, however, a business makes too little money, because of lack of energy or lack of initiative or because of indifference to technical and economic progress, that must not be regarded a just reason for reducing the compensation of the workers. But if the business in question is not making enough money to pay the workers an equitable wage because it is being crushed by unjust burdens or forced to sell its product at less than a just price, those who are thus the cause of the injury are guilty of grave wrong, for they deprive workers of their just wage and force them under the pinch of necessity to accept a wage less than fair. "
Unfortunately, all employers do not live up to their duties and would provide inadequate wages if they could. I wish all employers and employees would understand their responsibilities, for the responsibilities and duties are not all on one side. Reading both the above documents, particularly I think their condemnation of socialism as a solution to the problems of the world, would do all employers and employees a great deal of good.