New Keynesian models with unemployment and incomplete markets are rapidly becoming a new workhorse model in macroeconomics. Such models typically require heavy computational methods which may obscure intuition and overlook equilibria. We present a tractable version which can be characterized analytically. Our results highlight that - due the interaction between incomplete markets, sticky prices and endogenous unemployment risk - productivity shocks may have radically different effects than in traditional NK models, that the Taylor principle may fail, and that pessimistic beliefs may be self-fulfilling and move the economy into temporary episodes of low demand and high unemployment, as well as into a long-lasting .unemployment trap.. At the ...