I develop and estimate a general equilibrium model of oligopsonistic labour markets with task-based automation, in which labour market power and automation affect one another. Wage-setting power raises firms' marginal cost of labour, so firms with greater power automate more; automation in turn changes firms' relative size within local labour markets and so their wage-setting power. Labour market power misallocates both workers and tasks: more productive firms employ too few workers and automate too many tasks. Labour's comparative advantage across tasks governs the size of these distortions and whether cheaper automation strengthens or weakens the wage-setting power of more productive firms. Consistent with the theory, French manufacturers with greater labour market power hold more automation capital. Removing labour market power raises welfare by 6.3–9.0% of consumption; excluding automation understates this gain by 10–24%. Cheaper automation overwhelmingly benefits firm owners and raises the welfare cost of labour market power by 3–4%.