I couldn't resist making a few comments about a lesson that almost all econ majors sit through during their first week of class.
First, the graph:
A minimum wage is considered a price floor. In other words, it is a level below which the price of something is not allowed to fall.
Conversely, a price ceiling is a level above which the price of something is not allowed to rise. Think of rent control as a price ceiling.
Take a look at this graph of the labor market. The price of labor (shown on the y-axis) is of course, the wage rate. The point where the two black lines cross is equilibrium. At this point, the quantity of labor supplied by individuals is equal to the quantity of labor demanded by firms. Let's say it's 6 mil jobs at a rate of $15 per hour.
Think of the supply curve from your own personal perspective. It slopes upward because at higher wage rates you'll choose to work more, right? This is not always true due to the opposing influences of the income and substitution effects and something called indifference curves. However, we won't get into all that right now.
The demand curve can be thought of from the point of view of a firm. It slopes downward because the firm hires more workers at lower wage rates.
So it seems like a happy situation - no one is unemployed and the company has enough workers to meet product demand.
Now let's assume that legislation (a minimum wage law) is passed that requires firms to pay workers $20/hour.
At this wage rate, the demand curve tells us that the company only demands about 4 mil workers. However, the supply curve shows that 6 mil people are interested in working (because they will get $20/hour instead of $15/hour). So we have demand for labor equal to 4 mil and supply of labor equal to 6 mil. What do you think happens to the 2 mil extra people who can't get jobs at the company? They are unemployed.
But if minimum wage causes unemployment then why do minimum wage laws exist? The answer has to do with many things but politics probably plays the biggest role. Politicians would never get elected if they said, "Let's get rid of minimum wage!" Another part of the answer is that a complete lack of unemployment is not desirable. This has to do with the different types of unemployment which I'll save for another post.
I'll leave you with one last comment: you can use the same reasoning to see how rent control leads to a lack of housing because at P = 10, demand for housing exceeds the supply of housing.
I'll also say that my motivation for posting this is as follows: when you're a scared, sophomoric freshman (sorry for the pun, I couldn't resist) and the only thing that makes sense in your life is your economics textbook, you tend to think this simple example is pretty cool. At least I did...