This paper estimates the price elasticity of demand for alcohol using Health and Retirement Study data. To account for unobserved heterogeneity in price responsiveness, we use finite mixture models. We recover two latent groups, one is significantly responsive to price, but the other is unresponsive. The group with greater responsiveness is disadvantaged in multiple domains, including health, financial resources, education and perhaps even planning abilities. These results have policy implications. The unresponsive group drinks more heavily, suggesting that a higher tax would fail to curb the negative alcohol-related externalities. In contrast, the more disadvantaged group is more responsive to price, thus suffering greater deadweight loss, yet this group consumes fewer drinks per day and might be less likely to impose negative externalities. Copyright © 2011 John Wiley & Sons, Ltd.