Final answer:
The old dollar is worth the same as a new dollar due to its characteristic of being stable in value, ensuring equal worth and purchasing power regardless of physical condition.
Step-by-step explanation:
The characteristic of money that explains why an old dollar is worth as much as a new one is that it is stable in value. This means that whether the physical bill is old or brand new, it retains its value and purchasing power. The idea of fungibility, where units of a good such as dollars are interchangeable and each unit maintains equal value, ensures the value stability of money across different physical conditions. Money as a store of value holds onto value over time, thus an old dollar will generally be worth the same as a new dollar.