This paper provides an analysis of the social consequences of people seeking to get ahead of the Smiths. All individuals attempt to reach a higher rank than the Smiths, including the Smiths themselves. This attitude gives rise to an equilibrium in which all individuals have equal utilities but unequal (gross) incomes. Due to a rat‐race effect, individuals devote too much energy to climbing the social scale. However, laissez‐faire equilibrium is an equal‐utility constrained social optimum. Conversely, a utilitarian social planner would not choose utility equality. Unexpectedly, this social ambition theory fairly well accounts for empirical intermediate wage inequality.