Modeling Social Welfare Functions Aligned with Income Taxation

Objective: This study aims to develop and apply two advanced social welfare functions that enhance sensitivity to income inequality and risk aversion, focusing on improving the welfare of lower-income groups in the context of income tax policy design. Methods: The study critiques classical social welfare models—such as utilitarian and aggregative approaches—for their limited responsiveness to inequality and social behaviors. It introduces two alternative frameworks: i) A function based on the Atkinson inequality index, capturing societal aversion to income disparities. ii) A function utilizing constant relative risk aversion (CRRA) utility, modeling individual welfare under income volatility. These models evaluate the effects of varying income tax rates on overall social welfare, accounting for average income and its distribution across societal strata. Results: The analysis shows that increasing income tax rates across all income groups reduces social welfare due to lower post-tax incomes, even when redistribution is intended. Individuals with higher levels of risk aversion experience greater welfare losses, emphasizing the importance of incorporating inequality sensitivity and risk aversion into policy design. Conclusion: The proposed social welfare functions offer more robust analytical tools for optimizing income tax policies. They promote equitable income distribution and improved social welfare by integrating distributive justice and risk-averse behavior. These models provide practical guidance for policymakers balancing economic efficiency with social justice.

کلیدواژه ها:

Atkinson ، constant relative risk aversion (CRRA) ، social welfare function ، Utility Function