This paper develops a tractable version of the Lucas and Prescott (1974) search model. Each of a continuum of industries produces a heterogeneous good using a production technology that is continually hit by idiosyncratic shocks. In response to adverse shocks, some workers search for new industries while others are rest unemployed, waiting for their industry's condition to improve. We obtain closed-form expressions for key aggregate variables and use them to evaluate the model's quantitative predictions for unemployment and wages. Both search and rest unemployment are important for understanding the behavior of wages at the industry level.