If you think you can write an answer that is more complete, clearer, more rigorous, better supported by evidence, or that otherwise improves on an existing answer then you should do so. You should do this even if there is some overlap with a pre-existing answer.
The purpose of this site is to ensure that the best possible answer for each question gets posted. Absolutely the best way to achieve that is to have people posting improvements on existing answers when they see the opportunity to do so. In fact, the behaviour is actively encouraged by the stack exchange networks, which uses the number of answers per-question as a metric for evaluating the success of the site.
The whole reason for having a voting mechanism on the site is so that the community can choose the best answer and drive it to the top so that it is also the most visible. Nobody will feel offended if you try to improve on an answer they wrote (because everyone here understands that this is a collaborative effort to produce the best economics resource that we can). Unless an answer is an exact duplicate (in which case it should be flagged as spam), each answer should be evaluated on its own merits. An answer should be down-voted only if you think it is wrong, misleading, or fails to address the question. An answer should be up-voted if you think it does a good job of answering the question. If there is more than one answer that does a good job then you should up-vote all of them.