This paper is concerned with the problem of wage stickiness within the frame of the classical Goodwin's model. The first part of the paper is devoted to a critical review of some recent contributions on the effects of time delays on the labour market. In particular we concentrate on two important papers by Farkas (1984) and Farkas and Kotsis (1992). In the second part we use some results by Farkas to show how persistent periodic behaviours can arise when we combine the assumption of wage stickiness with that of an endogenously determined supply of labour accordingly to the "discouraged worker" hypothesis. Our discussion shows that an apparently reasonable assumption by Farkas and Kotsis suffers of theoretical inconsistencies with respect to Goodwin's frame.