I undertake a political economy exercise of a type described in John Rawls' A Theory of Justice; namely, one in which economic institutions are judged by how well they match the key principles in theories of distributive justice. My main contention is that such an exercise is integrally related not only to economics in general but to empirical economics in particular. I argue that most standard theories of justice place a large weight on self and social respect and that such respect has alot to do with the position a person holds in the productive process - their wage and employment outcomes. That, in turn, means that assessments of justice in the real world hinge critically on how labour markets actually function in assigning wages and employment. The answers to these questions are ultimately empirical. I explore these ideas by examining one particular institution (the minimum wage) in relation to a set of the most prominent recent theories of distributive justice. This exercise leads to a different emphasis on what minimum wage related outcomes need study, and to a claim that minimum wage setting is related to standards of fairness defined relative to the location of the low skilled wage distribution.