We develop a methodology to sign output distortions in the random participation framework. We apply our method to monopoly nonlinear pricing problem, to the regulatory monopoly problem and mainly to the optimal income tax problem. In the latter framework, individuals are heterogeneous across two...

The Friedman rule states that steady-state welfare is maximized when there is deflation at the real rate of interest. Recent work by Khan et al (2003) uses a richer model but still finds deflation optimal. In an otherwise standard new Keynesian model we show that, if households have hyperbolic...