The gender and ethnicity pay gaps are well publicised for academics. The majority of research relies on observations representing a point in time or uses models to consider a standard academic lifespan. We use a stochastic mathematical model to ask what drives differences in lifetime earnings of university academics and highlight a new question: how best should we quantify a working lifetime? The model observes and accounts for patterns in age when entering and leaving the workforce, and differing salary trajectories during an academic career. It is parameterized with data from a national dataset in Aotearoa New Zealand. We compare the total lifetime earnings of different gender and ethnicity groups with and without accounting for the different lengths of time spent in academia. The lifetime earnings gaps are considerably larger when we account for different hiring and leaving ages. We find that overall, for every ethnicity, women have shorter careers and are more likely to leave academia. All minority ethnic groups - and women - earn considerably less than their male white, European colleagues.