Abstract: The purposes of this paper are twofold. First, we construct and estimate a joint discrete structural model of labour supply and child care demand for partnered women with preschool children using the ‘in-confidence’ version of HILDA. As a methodological innovation, we impose a quantity constraint that the number of total child care hours (formal plus informal child care) is at least as large as the labour supply of the mother. Second, using simulations, we estimate the gross and net child care price elasticities for all mothers with preschool children and for various demographic sub-groups to shed light on labour supply behaviour and child care demand of women across income levels and socio-economic characteristics.