Probably little to nothing while adding a huge boom to the economy of the state selected. All the construction to house government workers, the restaurants and other venues the politicians would want, road building, you-name-it, in support of the new government buildings and infrastructure would be a huge boon to states that are right now economic small fry. Think of the money saved when Amtrak ends much of its east coast service because nobody's using it any more. Or, the increased revenues that air travel into the new capitol would occur.
You end up with one more failed Democrat city state on the East coast while the mid west flourishes.
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