This article examine the theoretical meaning of the elasticity of hours to wages accounting for Labour demand in an on-the-job equilibrium search model framework. A firm posts part and full-time job offers as a result of the trade-off between its demand variability, its wage costs and its hiring costs. Utility as a function of wages and the number of weekly worked hours is the criterion workers consider when accepting or rejecting job offers. We prove the existence of a Nash equilibrium, in which all firms hire both part- and full-time workers. Simulating the model, we show that the relationship between hours and wages depends dramatically on the firm's demand shape parameter and not on the individual preference for leisure.