What does "TV-L (E14, 100% position)" mean in terms of gross and net pay? What lifestyle does this buy you in Berlin?
This is in the context of a postdoc at a research institute.
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(This is maybe more suited to be a comment than an answer, but I don't have enough reputation to leave comments.)
About the phrase "100% position" in your question: This means that once you have followed the instructions in other answers and comments to identify the amount of money which corresponds to E14 on the TV-L payscale, then your gross pay is 100% of the amount labelled Brutto, and your net pay is 100% of the amount labelled Netto.
The reason this is explicitly stated is because other types of positions, such as 50% position or 65% position, also exist. I don't believe this is ever the case for postdocs, but it's the norm for PhD students. For example, a PhD student might have a "TV-L (El3, 50% position)", meaning that after one identifies the amount in the TV-L table corresponding to E13, the gross pay is only 50% of that amount.
A tip for reading these German payscale tables: the levels E1 to E15 are related to what sort of job it is and how qualified you are. PhDs and postdocs are at the E13 and E14 levels. For each of these levels, there are sub-levels 1 to 5 or 6, relating to how long you have occupied a position at this level. Over the years, you progress automatically up these levels 1 to 5 or 6
You are right that TV-L is a civil servant payscale. Postdocs commonly are placed in the E-13 or E-14 scale, where the latter is higher (but usually comes with more responsibilities). The gross pay starts at just under 3579.34 EUR per month for Berlin. Very recently the pay scales have been renegotiated, so I believe it might have gone up a bit. This amount is the first step in the scale, depending on your experience you might start at a higher step.
The net amount depends on your specific circumstances, for example if you are married and if you are a member of a church. For single persons that are not registered with a church the net amount is around 2100 EUR a month. This includes health insurance. You should be able to live decently in Berlin for this money.
The details can be found on the Öffentlicher Dienst website (in German, but you would want the table at the bottom).