Yes they have to pay market rates. Suppose they don't. They declare the job to be worth $2/hour, which they can do because minimum wage is just a law the gover

Yes they have to pay market rates. Suppose they don't. They declare the job to be worth $2/hour, which they can do because minimum wage is just a law the government can change. Nobody takes the job. Now what? Those job openings go unfilled forever, literally forever, until the government decides to pay market rate. The only way to pay below market rate is conscription. The government could draft people, forcing them to do the job. If people are free to leave, they are getting market rate.