Really great work lads, this stuff and some of the other posts show you're all working really hard. Hopefully this will be a good patch.
As an economist, I thought I'd chip in on the productive efficiency point.
So we apparently had some inquires about the exact formula used for our new production efficiency growth. Currently (and may well be subject to change) the daily production growth is calculated as y'=((1+m)/(k*y))*(M/100)^2. Where y' is the daily efficiency change, m is efficiency gain modifiers, k is a constant (currently 0.1), y is the current production efficiency and M is your Max efficiency. We're aware that the scaling to Max efficiency but not minimum efficiency will somewhat penalize growth at lower techs but don't neccessarily see this as a problem.
Your current production efficiency as a function of time is a discreet function but can be approximated as a continuous function (takes a little bit of differential calculus). You then arrive at y(t)=sqrt(20*m*t*(M/100)^2+100) where t represents the number of elapsed days. This will however overshoot the actual growth curve somewhat.
(In math terms we are essentially taking the left hand Riemann sum of this functions derivative and since the derivative is monotonously deceasing the left hand sum is smaller than its primitive function (that is, the continous function))
This is only the current formulas and may well be subject to change before release.
This is very interesting, as is your current graph. It's much more accurate than the previous formula you had. It's not a linear process and the rate at which efficiency is gained should begin very rapidly then exponentially slow down.
I would question the need for a cap at all. It definitely really does not make sense in a roleplay sense ("Boss! We've made our final improvement to the efficiency of tank production!" "Excellent, the Minister will be delighted to hear that tank production is now stunted."), but also in a gameplay sense - that certain industrial zones and production lines become incredibly efficient over the war did definitely happen, and this is why the Zero, the T-34, and the Panzer IV were all produced right up until the end of the war, to take only the most famous examples.
There is an elegant solution to both of these problems, and happily it emerges from a paper written about military aeroplane manufacture from 1936.
The full article is here (currently behind an annoying paywall sadly, but you can google the title to find references to it) and the jist of it is that as aggregate production of the factory line doubles, the marginal cost of each aeroplane falls by a constant 10-15%. So, assuming the constant is 10, your second aeroplane is 10% more efficient to build than the first one, the fourth is 10% more efficient than the second etc. This is clearly a logarithmic process, and it is known as experience curve theory.
For the maths behind it, check
this paper out, specifically Fig. 3. The constant doesn't have to be the same for each process, and you would need to twiddle around with it with different laws, techs, and products - which provides opportunities for different strategies and fun! This would provide an historically accurate and economics-based model for production. No idea about game balance though, and I'd be interested to see how the game handles it if you do give it a go!
Incidentally, the model is cute for business management types, but the really useful economic stuff is implicitly because the constant is constant for any given tech, it allows us to predict the future efficiency and therefore adoption of technologies. For example, given aggregate output of solar power, you can predict at which point the $ per kW/h of solar energy is equal to things like coal - currently we're on track for that by 2030, so fingers crossed...