Using the institutional theory of transaction costs, I demonstrate that the assumptions of the competitive labour market model are internally contradictory and lead to the conclusion that on purely theoretical grounds a perfectly competitive labour market is a logical impossibility. By extension, the familiar diagram of wage determination by supply and demand is also a logical impossibility and the neoclassical labour demand curve is not a well-defined construct. The reason is that the perfectly competitive market model presumes zero transaction costs and with zero transaction costs all labour is hired as independent contractors, implying that multi-person firms, the employment relationship and labour market disappear. With positive transaction costs, on the other hand, employment contracts are incomplete and the labour supply curve to the firm is upward sloping, again causing the labour demand curve to be ill-defined. As a result, theory suggests that wage rates are always and everywhere an amalgam of an administered and bargained price.