Final answer:
The homeowner is demonstrating the concept of Ricardian equivalence, which suggests that rational private households may offset government saving or borrowing. This theory states that any change in budget deficits or surpluses would be offset by a corresponding change in private saving, with no effect on physical capital investment or trade balances.
Step-by-step explanation:
The shortcut relating to "the rational republic" that the homeowner is demonstrating is the concept of Ricardian equivalence. This theory suggests that rational private households may shift their savings to offset government saving or borrowing. If Ricardian equivalence holds true, any change in budget deficits or surpluses would be completely offset by a corresponding change in private saving. Therefore, changes in government borrowing would have no effect on physical capital investment or trade balances.