An analysis of the dynamic behaviour of earnings distributions is conducted here in three ways. First, the method of dimensional analysis, in the context of Buckingham's Pi theorem, is employed to demonstrate that earnings distributions, which are almost always dynamic in character, should, under certain conditions and a special coordinate transformation, be self-similar and time-invariant. Application of the theorem to some empirical data, pertaining to Canadian income, fully confirms this finding. Second, an economics-based model, incorporating the concept of a shock-free economy in competitive equilibrium, is developed to provide an intuitive account of the conclusions reached above. Testing the model's predictions against data once again yields satisfactory agreement between the two. The model is finally extended to account for labour-force mobility across income brackets. The outcome of this, when compared with empirical data, could reflect the degree of homogeneity, and even discrimination, in a labour force.