First of all, an organization where almost 50% of the staff (900 out of 2,000) is engineering sounds cool -- even most "technology" companies are much lower than that. When you consider marketing, sales, admin, HR, upper management, support, etc. it's easy to see why. But that's beside the point.
As others have said (and I'm saying this both as a guy whose been pitched to, and been doing the pitch), in a healthy organization, it just comes down to numbers (dollars, man hours, etc.) When I've been the decision maker, if a decent business case can be made for the spending, assuming the money is even possibly available, I'll go to bat and advocate (or just approve if I'm in that position). Things like monitors, faster computers, etc. translate pretty nicely into engineer productivity. And I've usually had data to back that up.
When I've been the one asking for money, I try to give 2 or 3 different "models" or scenarios, with anticipated costs and anticipated savings (or increase in productivity), **along with** ways that I believe we can demonstrate/measure the benefit. Just saying "We'll be 25% more productive" is vague and wishy-washy. Saying, "We think we'll cut 3 weeks off of this next 4 month cycle" is something that can be measured during & after the effort. Obviously, you don't just want to make stuff up, but if the numbers are grounded in reality, go for it.
For the stuff I do, it's usually not computers or software, it's oscilliscopes, logic analyzers, simulators, etc. But the result is the same: better equipment/tools should have a quantifiable benefit. Then there is a rational, unemotional basis for discussion. And even better, when you don't get what you've proposed, and things go sideways (usually schedule), you've got a paper trail documenting what you proposed as an alternative.
