Many of our most pressing challenges, from combating climate change to dealing with pandemics, are collective action problems: situations in which individual and collective interests conflict with each other. In such situations people face a dilemma about making individually costly but collectively beneficial contributions to the common good. Understanding which factors influence people's willingness to make these contributions is vital for the design of policies and institutions that support the attainment of collective goals. In this study we investigate how inequalities, and different causes of inequalities, impact individual-level behaviour and group-level outcomes. First, we find that what people judged to be fair was not enough to solve the collective action problem: if they acted according to what they thought was fair, they would collectively fail. Second, the level of wealth (rich vs. poor) altered what was judged to be a fair contribution to the public good more than the cause of wealth (merit vs. luck vs. uncertain). Contributions during the game reflected these fairness judgements, with poorer individuals consistently contributing a higher proportion of their wealth than richer participants, which further increased inequality – particularly in successful groups. Finally, the cause of one's wealth was largely irrelevant, mattering most only when it was uncertain, as opposed to resulting from merit or luck. We discuss implications for policymakers and international climate change negotiations.