In countries with dual public and private healthcare systems, individuals are often incentivised to purchase private health insurance through subsidies and penalty. We use administrative data from Australia to study how high-income earners respond on both the intensive and extensive margins to the simultaneous withdrawal of a premium subsidy, and the increase of a tax penalty. We estimate regression discontinuity models by exploiting discontinuous changes in the penalty and subsidy rates. Our setting is particularly interesting because means testing creates different incentives at the extensive and intensive margins. Specifically, we could expect to see higher take-up of insurance coupled with downgrading to less expensive plans. We find evidence that the penalty – despite being large in value – only has a modest effect on take-up. Our results show little evidence of downgrading, which is consistent with a low price elasticity for the high-income earners we study.