I like the user3082 answer, definitely, make the price cheaper and you in the game.
After you managed how to build big structures in space - no problems with funding, no problems with people, there is a lot to sell: computer power, constructions in space, satellites, deep solar system missions, humans transportation, just plain materials in space. As being first you will get a lot of money from everyone.
But let say, shit happens, you will charge everyone, how to do.
You say, hey, earthlings, you have a problem with climate change, you fear your crops will burn out, the land will be covered by melting water from poles, winter is too harsh or too mild, sweating from hot summer. How lucky you are - call your government now 111-111-111, let them pay us, we will do the job.
So as for climate change countermeasures you establishing structure in L1 (Lagrangian point) which is 1'500'000km (0.01 a.e.) away.
The structure is a pretty big in size - something 14000 km in diameter. It does not have to be massive, and it does not need to be made from metal or be reflective. It can be made from transparent materials too - just focusing light so that it miss the earth - some sort of Fresnel lens maybe from graphene, prisms etc any optics also in the game. Using glass have advantage SiO2 is abundant, it's about 61-65 percent by element composition in the lunar regolith, with 28 percent of Mg, Al, Fe, Ti. So the lunar soil is a good composition for that - mirrors, optics, construction materials.
Let's say average construction is 1 ton per square meter. You have to have some control structures, to be able dim and illuminate different and precise areas of earth, but be not too precise, let say 5km spot is ok.
- 14000 km diameter, 1 tonne per square meter
This is a lot, 1.5386e+14 meters2, let say 1.6e+14
Energy consumption for glass production is around 9 GJ/tonne (from here, page 5), let say 10GJ/tonne
So production of entry construction needs 1.6e+24 J, mostly in form of heat. Probably it will be a reflective variant with a metal coating (easy like so, and optical prisms to compensate or even regulate the spectrum of light.
It is a lot of energy, but what helps is that we need just heat, that simplifies the process a lot. To be able to produce such structure in 1 Year, we need just 317 W of energy per square meter.
Holly moly, I have to recalculate:
10 GJ to produce 1 m2==1 tonne: 1e+10 / 365 / 24 / 3600 == 317.09791983764586504312 W
Very important number actually, specially in comparison with energy we have on earth orbit in space, which is roughly 1350 J/m2/sec or 1350W/m2
It is important because it means, such structure, when supplied with materials, may grow 4 times in surface area per year (4.2573 times actually, efficiency is already included in 10GJ/t, and it may be even better for larger quantities).
It actually may grow even faster because of a second limiting factor, after material supply, is energy collection. And heat collector is simpler structures, roughly speaking just thin foil of any metal available, from lunar soil, hundreds time less in mass and in production energy. Even or basalt-glass coated with metal will be lighter by mass per square meter and less energy to produce.
So exponential grow of our light management structure mostly limited by the speed of exponential grow of energy collector and our ability to get raw materials to that collector-processor for production.
Energy collector construction
Interesting work with glass, as you may see making desired form and complex, may be done simple, and without gravity, way bigger structures, and complex structures may be formed that way. Material for that is abundant, no need to refine, no need to process it chemically. Glass may be reinforced with metal, and other approaches to strengthen glass if needed.
As we need mainly heat, no need in solar panels, no precise machines in huge quantities, complex chemical processes etc, a just sheet of glass, coated with metal, which is evaporated by heat we collect.
Yes, you may have to have metal for actuators, simple processors to guide stuff. Actually, processors are not needed, an old Vacuum tube is ok for all parts. And it's a great excuse for some "miss-happening".
Where is my money
Forcing to buy energy is a least interesting part, of what you may do, but if you wish:
- as part of you care about earth climate and stabilizing temperature, you have to restrict solar energy input to some places. And as climate model is unstable and not linear and depends on bunch of factors, it so happens that our predictions show we have to dim that area, ahh there is your solar array oh so sad, but earth future is important etc etc. If model do not shows say its hardware malfunction, we working on improvements, but you know it's far far away.
You have to realize what it means, to have control over all light to earth.
It means not direct, but control over earth climate. Precise, flexible, fast control over the climate. We may not have good prediction model, if we may predict for a minute it's ok, it's good enough, we may just react and anyway we will get what we will. If you wish 1000 square km frozen in Sahara - it will be so. Wish melt iceberg - 1 sec phh done evaporated. Wish to disinfect large area from bio hazard - ultraviolet 1000000 times more then usual - everything will die in seconds. You wish for the pole to stay frozen, to save Amsterdam - freeze everything around that pole, freeze Gulfstream, make a big new pole in the middle of the pacific ocean(let it be night forever there). Control air flows mean control rain water distribution, and for Agriculture, it is very important.
When it's ready, or even in time of building, you may start to collect money. Forcing isn't interesting, because you will get way more just by doing what peoples like to buy, what they need and ready to pay.
- too hot to live - cool down that city. I heard it's a problem in some places in the US as an example. Some places in Saudi Arabia are harsh to live, as I heard, and with global warming they may be too hot to live at all (I do not know true or not, but +45 Celsius in shadow may be a problem) China have problems in some places, specially after building some dam and messing with river flows.
- save crops from burn out
- restore ozone layer - less cancer less medical treatment save money
- solar dependent energy generation - sell them 19 additional hours of sun shine, instead of average 5-6. It makes them 4 times more profitable, faster investment returns.
- Illuminate them 2-3-4 times more, and with the spectrum which is most efficient for them - less overall heat more energy production in less surface area. (it will just boost their energy productions 10 times with same equipment, so they may sell it cheaper than anyone - who will not cooperate, will be just out of business)
- boost crop productions, extend grow period, create 2 seasons for vegetables to grow. They will get twice crops as usual, or same in less space.
- boost fish food grow in oceans - bust fish production.
Just take money from countries, they all have problems which may be solved with control over solar light.
Just tax counties by 0.1% of their GDP for climate solving problem. It will be 70'000'000'000 $ per year. For everything else charge separate - I bet it could be done at least 10 times more such way.
Stability in L1.
To keep that structure in L1 reactive mass is not needed. Any perturbation will grow e times (2.718) in 23 days. That is true for a point mass, small objects. It means if the object is off by 1000km from L1 point position, in 23 days it will be off by 2718 km, 23 days later by 7389 km, 20000 km in first 2 months. Farther object is from L1, relatively bigger is the force. L1 is influenced by Venus(something around 300km in 23 days on closest approach), Mars, Jupiter, sun movements and so on.
That is true for this large structure too, but it has more control over that situation. Сounterweights on tethers will help in the situation. It's pretty complex stuff and I haven't calculated it deep enough to make oversimplification from results - but looks doable. Force it self is tiny, in absolute values - so even not strong materials will be ok for that all.
- moon mining for building such thing is a separate topic, and probably most tricky part here, doable, but I will probably stop here.