Except power itself is determined by supply and demand. Employers have gained more power precisely because of the increased labor supply (more women, more robots, more foreign workers) that is also responsible for stagnant wages.
The power, of course, comes from the need for others to have association with that person/business. In the current market, if one employee doesn't like the terms and conditions of the job, there are many others who will be quite happy to take their spot. This gives the employer leverage as employees want to be employed.
However, if there were actually more employers than employees, then the reverse would be true. Employees would be free to treat employers however they wanted, and force them to pay more money, without repercussion since if the employer walks away, there would be many more willing to take the worker. This gives the leverage to the employees as employers want employees.