Minimum wages regulations set a floor on the wage employees are legally allowed to pay. This would seem a good thing if it enabled employees to earn more. The Liberty Fund hosts the online Concise Encyclopedia of Economics, and this entry on Minimum Wages provides an overview of arguments for and against, along with economic analysis.
Here is a LearnLiberty video by George Mason University economists Don Boudreaux on the debate over whether wages in the U.S. have somehow stagnated in recent years.
Debates over just wages have swirled for centuries, though over that time industrial wages have risen dramatically. Average wages and disposable income are significantly higher now than they were in the 1980s when Milton Friedman's influential Free to Choose series was shown on PBS nationwide.
Below is Milton Friedman briefly discussing minimum wages laws. Friedman outlines the economic consequences of minimum wage laws and notes that most such laws are passed by an alliance of well-meaning reformers working with less well-meaning special interests who expect to benefit from the new law. In the case of minimum wages, labor unions support these regulations to protect union jobs from competition from lower skill nonunion workers willing to work for less.
Here is the full "Who Protects the Worker?" episode from Milton Friedman's 1980s Free to Choose series. The first 28-minutes feature Friedman explaining the classical liberal arguments for free labor markets with wage rates set by supply and demand rather than government regulators.
A spirited debate on Friedman's video begins at 28:15 at the University of Chicago with scholars both in favor and those opposed to free-market reforms of labor markets.
The then-young economist Walter Williams is featured in the video debate over minimum wages laws. A June, 2014 article by Williams, Politics of Minimum Wage is here.
Here is a energetic debate among Walter Williams and two minimum wage advocates including Charles Rangel from a public television debate.