What businesses are not bound by law to pay minimum wages?
The only one I can think of is the food service industry. Waitresses and waiters who collect tips as part of their pay aren't covered by minimum wage law for the most part.
Many, the cost of of running a small business is much higher than most individuals know/realize. Minimum wage, health insurance, employee benefits, etc. A big wheel grinds a little stone.
farm labor and a few others
Family owned small businesses with family as employees. I guess. I work for my mom and get paid 7.50 like once a month! Whenever an ad comes into Lehigh Valley Woman's Journal.