In this paper we estimate the elasticity of the labour supply to a firm, using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey. Estimation of this elasticity is of particular interest not only in its own right but also because of its relevance to the debate about the competitiveness of labour markets. The essence of monopsonistically competitive labour markets is that labour supply to a firm is imperfectly elastic with respect to the wage rate. The intuition is that, where workers have heterogeneous preferences or face mobility costs, firms can offer lower wages without immediately losing their workforce. This is in contrast to the perfectly competitive extreme, in which the elasticity is infinite. Therefore a simple test of whether labour markets are perfectly or imperfectly competitive involves estimating the elasticity of the labour supply to a firm. We find that the Australian wage elasticity of labour supply to a firm is around 0.71, only slightly smaller than the figure of 0.75 reported by Manning (2003) for the UK. These estimates are so far from the perfectly competitive assumption of an infinite elasticity that it would be difficult to make a case that labour markets are perfectly competitive.