Starbase Manufacturing/Research Bonuses Worthwhile?

I have an economic starbase next to earth with 14% bonus for manufacturing and research. I see this message 14% production/research bonus on the details tab for Earth but not sure how much it is contributing. The boost does not show up in the summary tab nor in the planet view directly. I counted that my industry has 44 mp and research has 40tp, exactly what i see when I examine/tabulate the buildings there. Where and how much is the 'boost'?

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It won't show on the Summary dialog of the planet (unless the effects are rolled into the totals at the bottom), but look in the upper RH corner of the Details page.  If the SB is in range you will see the 14% Starbase bonus listed. And that bonus does affect the output.

Note that the displayed output is the base output, multiplied by the 1 + (SUM of the bonuses), multiplied by the Economy slider setting, and probably a few other things.  Let's say you have a base output of 88, with existing bonus of 50%, for a gross output of 133.  Times the slider value of e.g. 30% yields 40.

Now add 14% bonus.  Gross output 144, times the slider value yields 43.  So the effect is +3 rather than the +12 that you might expect from multiplying 88 * 14%.

But to answer your question directly, heck yes Economy starbases are useful!  But they do eat a lot of production to get up, running, and protected, so I generally build them only where they can boost 3 or (preferably) more planets, barring a special case.  And I don't protect them with modules unless there is a lurking threat.

To test this, crank up the game. Note the outputs on the planet page. Destroy the SB, then run a turn and note the outputs again.  Quit without saving.