Alright. I can dig a hypothetical model. So here is what we should define very clearly in order to run some type of simulation.
What do you mean by the eventual crash? Do you mean the economy collapses? Or the civilization collapses? The difference being Detroit vs Ancient Rome. What size limit should we be talking about here? We might be able to assume this out, but it might end up being quite significant since, as I said, increase the measurement enough for local and it will go global. We also need to know what to hold constant. Should we hold technology, size of local, labor force, employment, etc constant so that we can assume them away?
Next, we need to define the relationship between the businesses and the consumers. Using predator prey language here: (A) we could model it in such a way that consumers are viewed as a "food source" for businesses thus larger businesses need more food. Or (B) we can model it where the businesses are a "food source" for consumers. While the first may be more appealing to you for visceral reasons, the latter also gives the ability to demo the dangerous effects of a monopoly. Furthermore, with this model instead of looking at direct interaction, we can state that change in income is what we are looking at rather than change in population.
I'll start off with something in (B) and go from there... something real simple until we get some more definitions. I'm not running this in maple yet so I don't have any results, but it might be something for you to work with.
I = income
p = price
L = local business
C = major Cooperation
I'=I(-p - L'+C')
p' = f(L,C) if L>0
or g(C) (marginal cost = marginal revenue for monopoly C) if L = 0
L' = L(a-bC)
so between L and C we have a normal loetka-volterra model with L acting as predator. However, we have consumer Income relying on both of these things acting as an overall predator. I didn't define a function for p' if L>0, but it could be something like a normal perfectly competitive market equation taking into account L and C or even a Cournot duopoly equation. The second half is just a monopoly price equation. I think it's likely that this could result in a crash since it can allow C to grow to infinity and this could cause the price to increase something awful which would cause income to drop.
However, there are some terrible things going on here. First, you are assuming a closed system. This removes gains from trade. Next, we are assuming perfect locality. Essentially, just as loetka-volterra assumes that if there are predators and prey, they are eating each other, we assume if the Corps exist, they are being used all the way to the demise of the economy. There is not really any punishment built in for overexpansion by C. There is obviously some type of barrier to entry, because if C really started charging a monopoly price when L left, then new L should pop up to offer cheaper services. What I'm saying is... we can find some set of equations to do anything... but trying to claim the equations prove anything by giving the variables names is not scientific. Also, as an economist, it hurts me when I see such outrage at places like wal-mart. I would highly suggest reading even fairly liberal economists such as Paul Krugman or Dean Baker. Even they will spout the great effects created by international trade and the terrible harm caused by economic isolationism.
As a small example of what I'm talking about here. Think about Detroit, MI. It was an economy built on employment at the major car companies. Then they closed shop and relocated to other places such as Mexico. This destroyed Detroit's economy. However, it wasn't the existence of the corps that destroyed it. It was the fact that they left. Detroit's economy would've been so much smaller if the businesses had never been there.