Can I publish an improved variation of a prior method or/and the results I found using it? I am doing economic analyses of natural resources based on processes seen in the real world (geology) for my PhD thesis. The model I have built is mostly inspired from an already well-established model in the literature, but my approach on getting economic values is quite different.

In details, the original model consists of 7 study cases for which data were taken from literature. The research estimates a type of resource to be explored/exploited worldwide. The concept is not really innovative and contains many approximations. Also, the assessment methods used to calculate economic values are basic mathematics. However, it is built on strong scientific bases and requires lots of understanding of natural processes.

My own model (inspired by the prior work) focuses on 4 of the same study cases, but I have made estimates for half of the worldwide potential occurrences for the same type of resource (plus another one). My study has better accuracy and uses different assumptions to get the economic values. My calculations for 3 of the study cases are different, except for 1 (I use different data and get different results though).

Question: Is it conceivable to publish my economic results, even if the modelling concept is similar to or inspired from someone's work?

I have cited the original research for comparing my results. The research is from a worldwide specialist who is well-considered in the scientific community. I would not want to have any conflict with him in the future.
Incremental improvement of research methods is a major part of the purpose of academic research, so yes, an improved variation of an existing method is absolutely a publishable result.  From your description of the research, it appears that you have undertaken a comparison of predictive accuracy for the original method and your variation, and this has good results.

Make sure your paper gives a good introduction and literature review, with a fair summary of existing methods and your points of departure for these methods. It is okay to put your method forward as being superior to the original method it is varying (assuming you can back this up with predictive results or other relevant evidence), but obviously you would write this in a way that is respectful towards the progenitor of the original method.  There is nothing offensive to a researcher in taking a method they have developed and varying it to improve its performance.  As long as you are not unduly critical of the original research, I see no reason that your research would set you in conflict with the original researcher of the method.  It is probably even worth listing the author of the original model as a suggested referee for your own paper.