The vast majority of economists believe the minimum wage law costs the economy thousands of jobs. The most fundamental principle of economics is 'supply and demand'. In the case of labor, this means that the supply of workers goes up as wage goes up, and the demand for workers by employers goes down as the wage goes up. For example, imagine a janitorial job was advertised for hire. If the wage were $100 per hour, thousands of people would want the job. If the wage were $1 per hour, you probably wouldn't find anyone to do it.
So if the government forced the employer to pay at least $7 per hour, the employer might decide not to hire a janitor at all, instead opting to have other staff member to pick up the duties. In this case a job would be lost because of the minimum wage. Another example is restaurant employment. A manager might have $10,000 in her monthly budget to hire bus persons. If the wage is set at $7 per hour, the manager may only be able to hire 10 bus people instead of 15. Setting a mandated wage limit disrupts market forces of supply and demand.
Just because there is no minimum wage doesn't mean companies can pay whatever they want. Would you work a dishwashing job that paid 25 cents per hour? Would anyone? If they raised the wage to $4 per hour, they might be able to hire a high school student. Consider some highly skilled jobs such as accountant, lawyer, and engineer. Do these people make $5. 15 an hour? Obviously, the answer is no. Market factors of supply and demand determine how many jobs are available and what each job would pay. In summary, as the minimum wage goes up, the number of people employed goes down.
When the minimum wage goes down, the number of people employed goes up. Keep in mind: the minimum wage only applies if someone is employed. Workers need a minimum amount of income from their work to survive and pay the bills. Someone working 40 hours per week at $5. 15 an hour will make about $800 per month after taxes. Rent alone can take almost the whole paycheck, especially in high-cost areas of the country like New York and Los Angeles (some states have higher minimum wages than the federal one specifically for this reason).
Then, you add in utilities, food, insurance, car payments, credit cards, and on and on. How can a person possibly survive on less? Businesses can better afford the money than citizens scratching to make ends meet. American businesses take in trillions of dollars every year. Is it too much to ask that they share a portion of it with the people responsible to bringing it to them? We've all read or heard stories of executives with multi-million dollar bonuses, even with companies that lose money.
A few dollars extra per hour for the poorest of the poor shouldn't hurt that much. History shows that businesses left unchecked will abuse their power. Why do you think labor organizations like the Teamsters, United Auto Workers, AFL-CIO, etc. have come into existence? A tight job market, especially during recessions, gives citizens the choice of accepting the terms of business or starving. A minimum wage gives business a reasonable rate that should be paid for the labor of others, whether skilled or unskilled.