Higher education is not just a signal of innate ability. At least a certain level of educational achievement (degree level, degree mark) is strictly required to perform a graduate job. School leavers fall into two categories, the rich and the poor. Ability is distributed in the same way in both groups. Graduate jobs are differentiated by quality. The output of each graduate job-worker match depends on the worker's ability and educational achievement as well as on the quality of the job. Individual wealth and ability are private information. Educational achievement and realized productivity are common knowledge. Graduates and graduate jobs are matched by tournament. In laissez faire, only the rich can buy enough education and enter the tournament. The poor are confined to the non-graduate labour market. This is doubly inefficient because some of the rich buy too much education, and some of the graduates have lower ability than some of the non-graduates. Student loans allow the more able among the poor to buy a higher education, discourage the less able among the rich from so doing, and bring individual education investments closer to their efficient levels. Unless the loan is large enough to allow a poor school leaver to invest as much, and thus get as good a job, as a rich one of the same ability, however, jobs of the same quality are assigned to graduates with the same education but different ability. Competition among employers will then result in poor graduates being paid a higher salary than rich graduates doing the same job.