Interesting question. At my old company, we used to have a guy for that, who was a freelancer like yourself. He used to work for the phone company and then branched out into that. I don't know how he determined his rate. I'm assuming that you've already tried doing some market research to find out about others in your area? Are you having problems locating other businesses who do that?

One idea: Once you've established a rapport with the client who said you were "cheaper", you could ask them who their other alternatives were, then research those folks. Perhaps ask them how they located those other businesses. Another crazy idea: Once you know who the other businesses are, maybe establish a friendship with them. Services like that who are in competition, aren't always adversarial. For example, referring clients to each other when over-scheduled.

Some google searches turn up pages like this... This page assumes that you your goal is to set your rate based on your own personal needs rather than based on the external market: https://www.creativelive.com/blog/how-to-calculate-freelance-hourly-rate-infographic/

In any case, I'll bet that your rate will be something that you change over time, as you discover more about your market, and more about your financial needs.

Good luck!