I've been living in Shenzhen, China for almost 1.5 years at the time that I write this. Since I've been here, I've been teaching private English, guitar and even some basketball lessons. Regarding tutoring prices, it varies among English teachers. However, you should not be afraid to charge a fair price.
I have a good American friend whose price is 250 RMB per hour (about $41 per hour) for private English lessons. He keeps very busy, though his market is definitely wealthier Chinese families. When I first started teaching English and guitar, I was content with 150 RMB per hour ($25). This is OK if you need to find students fast. And at that price, your schedule will likely fill up very quickly. However, once you become busy, you will likely want to increase your rate to 200-300 per hour. After increasing my rate to 200 (about $33 per hour), I didn't lose any students. Since I am no longer "desperate", I am now asking between 200-250 per hour for new students, depending on travel time, etc.
I have met some people who think 200-300 RMB is too expensive. Chinese English teachers often charge 100 RMB per hour, for example. However, native English speakers in China are in completely different situations than local Chinese English teachers. For example, I am sacrificing time with family and friends in America. I also have to purchase a Visa and plane tickets every year. This can be expensive.
Also remember that, as a native English speaker, you offer something unique in China. Your accent, knowledge of culture and knowledge of grammar are generally seen as optimal for those who want to learn proper English. If you have any college education, this should also be reflected in your price. For these reasons, your price should be higher than a non-native English teacher.
For group lessons, I feel a good price is 300-500 RMB per hour, depending on the size of the class. I have a friend who teaches in his apartment, and he always charges 400 RMB per class, no matter what the size of the class. This gives incentive for his students to find more people to bring to his class. Plus, he is making good money no matter what.