Should there be a federal minimum wage?

Should they leave the setting of a minimum wage up to state and local municipalities? If there wasn't a federal minimum wage would that allow more competition between state and local economies to attract workers? Instead of defaulting to the federal minimum wage, localized governments would have to set minimum wages to attract workers. If a small town had a set minimum wage that is higher than other areas, it would attract service workers to that area and allow for more selection for the businesses in that area. Would this help the economy and drive competition or would this further suppress service workers and weaken the economy?