cat licks hair off? Please help

cat licks hair off? Please help

My cat has been licking the hair off his stomach and legs for about a year now. It all started when we moved into a house that previously had cats. He is about 10 years old and has never done this before. I took him to the vet and he got a cortazone shot. This did not work. I read that he might be lonely so I bought a kitten. This worked great for about a month and the hair started coming off again. The vet then recommended I change his cat food. Once again I thought I found the cure but it only lasted about a month. Now he is bald on the stomach and legs and going for the front legs. I’m lost, I guess I might have to try a cat prozac or something. I’d appreciate any advice. Thanks