Under basic contract law, a contract is the law between the parties." If you are employing the instructors as independent contractors, and the contract is the law between you and the instructor, inspect the contract, presuming you have one, and if it doesn't contain a provision for this particular issue, and you have an established practice of not paying instructors for missed appointments, then you can't be compelled to be responsible for something so arbitrary as a student not showing up. If you don't have contracts drawn up for your business you should probably have a standard contract drawn up to protect you from these issues should they occur in the future.
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Ms. Eskinde is correct. Your contract will control this situation and if you don't have one....get one fast. You should see an attorney to have to draft one to suit your needs.Ask a similar question
I do not disagree with either of the answers previously posted, however, on a more practical note, how much could this fee possibly be? $50? $100? It is unlikely that anyone is going to take you to court over $100. It is possible, but extremely unlikely. In the event that they do, it will be small claims court where people routinely represent themselves, and a lawyer is more of an exception that the rule.
You should know that if you are sued in small claims court (or any other court) and you lose, the court may impose the court costs on you as well. So, it is not without risk.
Unless you are a huge business, a simple contract should handle these issues. For the matters arising before the contract, you should be able to work these issues out without involving the courts.