Since President Obama proposed an increase in the federal minimum wage in the U.S., from $7.25 per hour to $9 per hour and then index it to inflation, the debate has been raging about whether or not this would make low wage workers better paid or not paid at all (or in other words if they would get unemployed).
The short answer is that it would be a little bit of both, but with emphasis on little. To understand why we must first examine the issue theoretically and then look at current U.S. conditions.
Starting with theory, when a worker's pay is set on the free market, it will be no higher than the worker's (expected) marginal productivity and no lower than what the worker could get paid elsewhere or what the worker would feel is so low that not having any job is better (the latter is of course influenced by the extent to which the workers could live on for example unemployment benefits or welfare). The latter could be referred to as a worker's personal minimum wage.
For unemployed workers their personal minimum wage is higher than the marginal productivity employers think they might have for them, while for employed workers, the marginal productivity is equal to or higher.
When marginal productivity is higher than the personal minimum wage, the actual pay will be the result of a bargaining process and will usually come in somewhere in between. What then happens if the government steps in and legislates a legal minimum wage?
That depends. If the legal minimum wage is lower or equal to the current pay level, nothing happens at all. If it is higher than current pay but lower than marginal productivity then workers get higher pay. If it is higher than marginal productivity, workers lose their jobs.
Since minimum wages are usually far below median pay, for most workers nothing happens. For the small numbers that are affected some will receive a raise, while others will lose their jobs. The exact proportion of workers who are unaffacted, of workers who receive higher pay and of workers who lose their jobs depend on the specific conditions in each specific country (or state or city) and each specific period of time and will therefore differ between different locations and different periods of time
With average hourly earnings currently at $23.78 per hour and with average pay even in the lowest paid sector, "leisure and hospitality" at $13.37, it is obvious that raising the minimum wage would only cause minor job losses. But it is also obvious that would only raise take home pay for a very small number of workers.