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Really, the answer to your question is self-evident. If you are being underpaid for a person with you education, experience and abilities, then you will be able to find another position that pays you what you are actually worth. If not, well…..
I’m not in CA, so I don’t know the particulars about cost of living and average wages in your field. Your credentials sound solid, but there are many, many people across the country with bachelor degrees and doctorates who are struggling to find jobs. You have three years of experience. That’s next to nothing in the big scheme of things. Because there are, at the moment, more qualified potential employees than positions available it is, unfortunately for you, something of a buyers market as you noted. However, if you are able to show that you are somehow a superior potential employee that the other candidates for a given position, you should have a superior bargaining position when it comes to wages. Look in the local trade pubs and see what range of salaries are offered for equivalent positions. If an employer is unwilling to pay you what you think you are worth, well then, one of you is wrong. If you are confident that the one who is wrong is not you, then you can give your notice and move on to greener pastures. If you are not so certain, well, then, I suspect you will not be as inclined to take a hard line at the bargaining table.
Good luck to you. I do not know whether you are being underpaid or not, because I don’t know you or the specifics of your job market. I do know people who have impressive credentials on their resume who are doing worse than you right now. The thing is, if you truly feel that your employer undervalues you, you will never be happy there, and every day that you go into work you will feel resentment. You need to resolve that, one way or another.