I remember having epic discussions about this topic because I didn't use to believe what people told me, simply because it didn't make sense from a mathematical point of view.
I had to learn this the hard way, and since I ventured in to the dark world of modding, I also understand why this is as it is.
See, between what is written in the description of an upgrade and what actually happens on pressing that upgrade, there is a world of difference. I can make the description of those upgrades read as : "your peasants will now harvest banana's", if you press that upgrade button, it will still have an effect on your stone collection, no matter what the description says.
Now, let's have a look at the technical explanation why these upgrades are not cumulative , as you would expect from a % increase.
These are the actual upgrade lines from the nation files:
AKA23SP A23 #POSITION 7 1 #LEVEL 1 AKA23AU #COST 2 GOLD 1550 IRON 3000 #TIME 500
AKA24SP A24 #POSITION 7 2 #LEVEL 1 AKA24AU #COST 3 FOOD 4200 GOLD 1550 COAL 12520 #TIME 500
Notice how it says, effect stone 200 and 400, not 200%, not + 200, but plain 200. This sets the rate of collection at this level in a given time frame.
Researching first the 400 and then the 200, well, it's clear, is actually decreasing the rate of collection.
So whatever has been written in the description is just plain wrong. It's not 100%, it's not 200%, it's not 300%, its not 400%, it's all just wrong. Simple as that.
What about food?
Ha, that, is different, read with me:
AKA01SP A1 #POSITION 0 0 #LEVEL 1 AKA01AU #COST 2 GOLD 322 WOOD 200 #TIME 500
AKA02SP A2 #POSITION 0 1 #LEVEL 1 AKA02AU #COST 2 GOLD 1522 WOOD 12400 #TIME 500
AKA03SP A3 #POSITION 0 2 #LEVEL 1 AKA03AU #COST 2 GOLD 1330 WOOD 32400 #TIME 500
AKA04SP A4 #POSITION 1 0 #LEVEL 1 AKA04AU #COST 2 GOLD 522 WOOD 1400 #TIME 500
KUZ01SP K1 #POSITION 0 0 #LEVEL 1 KUZ01AU #COST 2 GOLD 100 WOOD 400 #TIME 500
Melnica(sp)GETRES M1 #POSITION 2 2 #LEVEL 1 Melnica(au)GETRES #COST 2 FOOD 750 GOLD 250 #TIME 500
Melnica(sp)GETRES2 M2 #POSITION 2 2 #LEVEL 2 Melnica(au)GETRES2 #COST 3 FOOD 40600 GOLD 3350 IRON 2900 #TIME 500
See how here there is a + in front of the parameter? That should explain why the above logic doesn't apply for the food upgrades. The food upgrades are cumulative.
Morale: the descriptions are highly deceptive and written by someone who had no clue about what was programmed, including the stuff written down on the site here about resources, which I urgently need to update correctly.
There , clear?
I hope you all noticed that researching the second and third academy upgrade for food are a pure waste of money as they are costing lots of wood and yield little result compared to the 4th academy upgrade and the blacksmith upgrade for food.
EDIT:: and why on earth is this thread labeled "trick at market" while its about stone upgrades?