Critics point out that the prince, on his income, should be paying tax.

【翻译】批评者们指出，根据其收入王子应该纳税。

on 可以表示“凭着，依靠，根据；以…为基础”之意。例如：

Sure he can swing a new car on his income.  按他的收入，他是买得起一辆新车的。

I had to live on bread and water when I was a student.  我上大学时只能靠粗茶淡饭过活。

We depend on the radio for news.  我们靠收音机听新闻。

You can't rely on his assistance.  你不能指望他能帮助你。

The story is based on historical facts.  这个故事是以历史事实为根据的。