Rotten Kid Theorem

The Rotten Kid Theorem, developed by Gary Becker, posits that if a household head is benevolent towards other members, even selfish individuals will act in ways that maximise the total family income, even if it reduces their own pre-transfer income. 

This happens because the "rotten kid" recognises that their own well-being (as determined by the benevolent head) is tied to the overall family's prosperity. 

In simpler terms:

• Scenario: Imagine a family where one member is very generous and cares deeply about the well-being of everyone else.
• The "Rotten Kid": Another family member is selfish and only cares about their own personal gain.
• The Theorem: The selfish member will still act in a way that increases the overall family income, even if it means they get less individually, because they understand the benevolent head will reward them for it. They understand their own happiness is linked to the family's success. 

Key aspects of the Rotten Kid Theorem:

• Benevolence: The theorem requires a household head who is sufficiently benevolent and cares about other members' well-being. 
• Self-Interest: Even selfish individuals are motivated by self-interest, but in this case, their self-interest is tied to the overall family's success. 
• Actions that Benefit the Family: The "rotten kid" will take actions that increase total family income, even if it means reducing their own share before the benevolent head makes transfers. 

Limitations:

The theorem's effectiveness depends on certain conditions, such as the household head's level of benevolence and the strength of the "rotten kid"s self-interest. In some cases, the theorem may not hold, especially if the benevolent head's actions are not perceived as fair or if the "rotten kid" is too resistant to the concept of sharing resources