Here is a few graphs I have made, I will add more at a later point, such as about building non industry districts after building a certain amount of industry districts. The caculations used to make the graphs are simplified, I caculated districts fractions rather than just whole districts and I assumed that each district have the same industrial output. Still I hope these may give an idea about the value of industry districts.

First is the cost of a normal district, like a makers quarter based on number of previous districts that have already been built, the cost increase seems to be rather linear.

Next is the sum of the cost of all districts built at the point which seems to increase like a power function. At 150 districts you have paid only about 1/3 of the cost of building the next 100 districts which showcase the dramatic cost increase of building many districts.

 Now we take a look at two other graphs, in those I assumed a scenario in which a city simply keep building maker's quarter. I assumed each maker's quarter produce a constant amount of industry and I used 5 different values, 10 industry, 20 industry, 40 industry, 80 industry and 160 industry per maker's quarter. Even if those last two sound unrealistic high, you can assume those numbers have been achieved with industry multipliers such as fusion power technology.

First graph show how many maker's quarter each industry output value manage up to 250 turns, as you can see it make quite a dramatic difference with industry output, high industry output mean many more districts can be built over the long run.

The second graph show how much industry the city produce per turn, this difference is even more dramatic. This make sense  logically as not only do more industry output per district mean we can build more of them, but each one produce more industry as well.

Now we look at what happen if we build industry districts up to x amount of turns, with x being the values of 10 turns, 30 turns, 50 turns, 70 turns and 100 turns. After which we build a non industry district, like research quarters. The graphs will show both total number of non industry district built up to 250 turns as well as how much output the non industrial districts have produced. Output is 1 per turn per non industrial district that should make it easy to calculate "like how much research have research quarters that produce an average of 10 research per turn produced up to turn x", this you can do by multiplying the output value by 10. Keep in mind that there are advantages of having industry which is not shown here, so building more industry districts than may look optimal according to these graphs is probably still a good idea such as being able to build infrastructure to boost those non industry districts.

However keep in mind these graphs use the same flawed fractional district and assume all districts are identical with constant values that never changes, so they should only been seen as an approximations.

First is for the case each industry district produce 10 industry per turn:

For the case of 10 industry, building industry district for 10 turns seems to lead to around turn 125 before losing the lead and falling behind. From turn 125 onwards the 30 turn build seems to lead but is about to lose it at turn 250 to 50 turns build. The 70 and 100 turn industry builds perform poorly here.

Now the case of industry districts produce 20 industry per turn:

I don't see much to say here as the situation look similar to the one seen in the case of industry districts producing 10 industry.

Next case, 40 industry per industrial district:

Again the case is quite similar to 10 and 20 industry per industrial district so I'm not sure there is anything more needed to say here.

Now we will look at the case of industrial districts producing 80 industry per turn:

Nothing unexpected, we this is the case we seems to get every time.

So now lets look at the last case, 160 industry per industrial district per turn:

I don't think we are surprised. In all cases the 10 turn build take the early lead which it lose around turn 150 after which turn 30 build maintain the lead, followed closely by turn 50 build. Turn 70 and 100 build start too late and thus fail to catchup even with turn 10 build. 

However these cases have serious limitations such as the industrial district having a constant value while in reality they are likely going to improve from maybe 10 industry early game to maybe over 100 industry per turn later in the game.

I think I made an error, I will fix it maybe in an hour. The error should be fixed now, I could have made more, but I hope not.

Yeah, that is difficult to account for, but I could attempt an open graph alternator by, for instance, supposing  that the productivity of our economic district increases by about one sector each rotation.

Hi, in case of anyone can find value here, below is an attemp at an illustration of the above posts and graphs, with very little maths

tl/dr it says in the first quarter of your game, using your city production to improve your city production is probably the best thing to do. whatever else you'll do after that, the added production bonus will allow you to do more of anyway. 

The later it goes after that first quarter, the less efficient it is and you should focus on what you really need (and no you don't need production. you want production to produce other things)

Basically producing an industry district 20 turns before the end of the game is probably dumb as it'll cost more than it would gain anyway, you'd be better off not doing anything (but you couldn't end the turn, could you?)

*example : if I start with building science districts, i'll get science. but If I build 1 industry district and then (more) science districts with the added production, I'll eventually gain more science at all. and it would even be better if I built 2 industry districts. his graphs says it's better if I build industry district until turn ~50 to 70

even though there are gross approximation and simplifications, This is an attempt to estimate that moment. it takes plenty variations, but the conclusion seems to point toward turn 50 or 70 ~25% of you game is roughly the moment at which you can actually consider building the things you want, and not 'i'll just focus on industry for now because it'll be better later