Instead of approval improvements you can build just more specialized improvements or farms and get great adjacency bonuses. Growth penalty is negated with adjanced food distributors and hospitals surrounded with farms. That's my point. You should just try make high approval forge world and compare its effectiveness to low approval one.
A planet's total output across the wealth, research, and manufacturing categories may be computed as
[total output] = (1 + [approval modifier] + [production modifier])*([flat production bonus] + [population-based production])*
(1 + [manufacturing fraction]*[manufacturing bonus] + [wealth fraction]*[wealth bonus] + [research fraction]*[research bonus])
+ [flat manufacturing bonus]*(1 + [manufacturing bonus]) + [flat research bonus]*(1 + [research bonus]) + [flat wealth bonus]*
(1 + [wealth bonus]) + [tourism] - [maintenance]
Flat manufacturing bonuses are rare; the only one I can think of is Relentless in the Malevolent tree, which is supposed to only apply to the homeworld but, due to a bug in the current implementation, applies to the homeworld and first colony. Flat research bonuses are slightly less rare, being available from the Ancient faction trait and from Quantum Leap in the Benevolent tree (unlike Relentless, both of these apply to all colonies). Flat wealth bonuses, as far as I know, are only available from Promethion Pleasure Parks, whose rarity is dependent on how much Promethion you can acquire and how much of it you throw into parks. Tourism is fairly negligible in my experience, being an order of magnitude or two lower than the gross income from wealth-specialized worlds, but is useful for counteracting maintenance costs on all worlds. All flat output bonuses tend to be fairly small relative to the production-based outputs, especially on specialized worlds. Modifiers to production are relatively rare but not necessarily difficult to obtain; Economic Rings are the most common and most easily obtained, giving +10% each, and can be stacked up to 12 times (bonuses stack additively; note that getting 12 Economic Starbases to affect a single planet is not necessarily practical, and might not be optimal depending on how this affects other planets), though there are also the level bonuses on the Thalan Hives (+5% production per level) and perhaps one or two other things that I'm forgetting.
At present, the population-based production may be computed as
[population-based production] = 2 * [population]^0.7
However, according to the patch notes for v1.02, this will change to be
[population-based production] = [population]
when v1.02 is released.
The approval modifier is defined by a set of points in the GalCiv3GlobalDefs.XML file, between which the game interpolates to generate the approval modifier. Currently, these points are (approval, modifier): (1, 0.25), (0.95, .2), (0.85, 0.15), (0.7, 0.05), (0.5, 0), (0.3, -0.05), (0.15, -0.15), (0.05, -0.2), (0, -0.25); the v1.02 patch notes suggest that the points (0.6, 0) and (0.4, 0) will be added to this list (or possibly replace some of the points already on this list).
As can be seen from the formula, and with knowledge about the terms not affected by approval, it can be seen that the approval modifier can have a very significant effect upon a planet's total output, especially in the absence of other production multipliers. Going from 50% approval to 100% approval has the same effect as increasing the overall output multiplier by 25% in the absence of starbases and flat manufacturing, research, and income bonuses.
