Public Health Considerations on the Optimal Sin Tax Under Consumer Heterogeneity, with Implications for Inequality in Health

We study the optimal choice of sin tax by a public health authority, when the consumption of a harmful good is unevenly distributed across the income distribution. The optimal tax level adjusts away from the level applied when heterogeneity is ignored, according to the degree of relative inequality in the income distribution, as well as non-linearities in the population health and deadweight loss functions. Drawing on findings from the literature on income distribution and redistribution, we compare the impact of the two tax levels on relative inequality in health and participation in unhealthy consumption. Under reasonable assumptions about functional forms, and independently of the distribution of income, we show that the heterogeneity-adjusted sin tax can increase both efficiency and health inequality.