RML: Supply of employment is not a linear entity, nor is demand. People must work to eat. Employers must hire people to have the resources to make lots of money.
In addition, the minimum wage only affects a certain class of job. A computer company will not be able to hire anyone at the minimum wage to hack kernels, because that is a different market to the one in which the minimum wage plays a role.
In the market where the minimum wage might play a role, it's more like perfect competition. There are N low-wage job positions to be filled, and an infinity of people willing to fill them. At 5 dollars an hour, all N will be filled. And at 6 dollars an hour, all N will be filled.
The question is what is the minimum quality of life we as a society want the bottom wage earners to have. If a mother has to get 2 jobs at your alleged point of equilibrium just to be able to pay rent & buy groceries, that's a problem. The minimum wage is set very simply - what is the minimum someone needs to be able to be paid to survive? If people are working full-time for less than that, that's society's problem.