Using administrative linked employer-employee data for Norway we estimate the impact of changes in tax subsidies for union membership on individuals' membership probabilities. Increased subsidisation of the union good increases union take-up, while increased union fees reduce the demand for membership. The price elasticity of demand for union membership is - 7 percent in 2012 (the last year for which we have data) though effects are heterogeneous across types of worker. In the absence of the hikes in tax subsidies and holding workforce composition constant aggregate private sector union membership density would have fallen by 5 percentage points between 2001 and 2012. Since membership fees are a substantial part of unions' total revenues the findings have important implications for unions' viability. They are also significant because union bargaining strength, which is often proxied by union density, affects a range of social, economic and political outcomes.