It is it not also true that the hypothetical family would never go bankrupt if we assume they could pay in debt instruments indefinitely?
Instead of balancing a checkbook, they could simply buy groceries with IOUs. Of course, in an emergency scenario those IOUs would be heavily discounted by creditors seeking to make good on the debt. In this scenario, the price of gold as denominated in discounted IOUs would be much higher.
The entire exercise and the term emergency illustrates that there are indeed limits. This is the reason why they claim to hold gold.
Instead of balancing a checkbook, they could simply buy groceries with IOUs. Of course, in an emergency scenario those IOUs would be heavily discounted by creditors seeking to make good on the debt. In this scenario, the price of gold as denominated in discounted IOUs would be much higher.
The entire exercise and the term emergency illustrates that there are indeed limits. This is the reason why they claim to hold gold.