I figured that the economic capital does not at all effect the other existing economic instllements such as stock markets. It only givs a bonus of 50 % more tax. So to get the most effect it should be placed on the planet with the highest population, right?
Yep.
I also tend to think that you need the economic boost from the economic capital in the beginning of the game and hence I alway places it on earth and then try to grow the population to an economical feasible level.
Yep again.
The Economic Capital has twice the benefit of a stockmarket, costs a bit less than two stockmarkets and requires no maintenance. Also you usually have the tech to build your Economic Capital (Trade) earlier than you research Stock Markets.
However depending on how you "build" it, it's not necessarily that great of a deal. If you produce your buildings the old fashioned way via social production with factories then once you have nothing better to build on your homeworld then you may as well queue up your Economic Capital.
However if you're like me and "build" most of your early game buildings by rush buying them on a long term lease then it's usually not worthwhile to build it and then try and get your homeplanet population up. In this case you would want to wait until your homeworld pop is high enough to make it worthwhile to purchase the building. Also in the grand scheme of Super Projects, Trade Goods and Galactic Achievements your Economic Capital is rather low on the totem pole.
The bottom line is that while your Economic Capital is basically useful and something you should build sooner or later it's far more beneficial to build something like Harmony Crystals or Ultra Spices that give a global morale bonus allowing you to increase taxes on *all* your planets instead of a building that gives you a minor economic bonus on a single planet.