If productivity increases more slowly for services than for manufactured goods, then services suffer from Baumol's cost disease and tend to become relatively more costly over time. Since the welfare state in all countries is an important supplier of tax financed services, this translates into a financial pressure that seems to leave policymakers with a trilemma: increase tax distortions, cut spending or redistribute less. Under the assumptions underlying Baumol's cost disease, we show that these dismal implications are not warranted. The welfare state is sustainable, and there is even scope for Pareto improvements under Baumol's cost disease.