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I present a model where firms decide what types of jobs to create and then search for suitable workers. When there are few skilled workers and the skilled-unskilled productivity gap is small, firms create a single type of job and recruit all workers. An increase in the proportion of skilled workers or skill-biased technical change can create a qualitative change in the composition of jobs, increasing the demand for skills, wage inequality, and unemployment. I provide some evidence that there has been a change in the composition of jobs in the United States during the past two decades.