In military affairs, there are economies of scale. An army of warriors makes conquest cost-effective. There are also taxation advantages. An army of tax collectors makes tax collection cost-effective. “Hand over your money” is more effective. Pretty soon, you’ve got an empire.
But there is a law of bureaucracy that applies to empire. At some point, it costs more to administer the bureaucracy than the bureaucracy can generate through coercion. Then the empire begins to crack. It cannot enforce its claims.
So, the growth of empire has economics at its center: economies of scale. The fall of empire also has economics at its center: economies of scale.
I think this process is an application of the law of increasing returns. In the initial phase of the process, adding more of one factor increases total output. But, as more of it is added, another law takes over: the law of decreasing returns.
Example: water and land. Add some water to a desert, and you can grow more food. Add more water, and you can grow a lot more food. There is an accelerating rate of returns. The joint output is of greater value than the cost of adding water. But if you keep adding water, you will get a swamp. The law of decelerating returns takes over. Add more water, and the land is underwater. You might as well have a desert.
This law applies to power. Add power, and you generate more income. But if you keep adding power, expenses of the bureaucracy will begin to eat up revenues. Resistance will also increase: internal and external. The system either implodes or withers away.
With only one exception in history — the Soviet Union in 1991 — empires have not gone out of business without bloodshed.