We treat money as separate categories, not as something fungible.
A dollar saved and a dollar from a year-end bonus are worth exactly the same in the bank account, but not in the mind. We tend to assign money to separate mental categories (salary, bonus, savings, casino winnings) and treat each one with different rules, instead of seeing it all as one interchangeable pool.
Imagine you bought a $10 theater ticket, and when you arrive you realize you lost it. Most people hesitate a lot before buying another ticket. Now imagine that instead you lost a $10 bill on the street before buying the ticket. Almost everyone still buys the ticket. The objective loss is identical in both cases, $10, but in the first scenario the money was already "assigned" to the mental category of "evening entertainment," and spending another $10 there feels like duplicating that specific expense.
Categorizing money into mental accounts simplifies self-control (it's easier not to touch "the house savings" if it exists as a separate category), but it also leads us into inconsistent decisions, like borrowing at a high interest rate while keeping savings earning a low rate in a separate account.
Source: Thaler, R. H. (1985). Mental Accounting and Consumer Choice. Marketing Science, 4(3), 199-214.
An "emergency fund" kept separate from the checking account, or a benefit framed as "extra money" instead of "part of your salary," change how it's spent or saved, even when the total amount available is identical.
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