This paper examines the impact of income growth and income inequality on household saving rates and payoffs in a non-cooperative game where each player’s payoff depends on her present and future consumption and her rank in the present consumption distribution. The setting is a pooling equilibrium with three clusters of successive income groups, each cluster having its own present-consumption standard and rank in the present-consumption distribution. In this way the analysis addresses the saving behaviour and welfare of three social classes: the lower, middle and upper class. Explanations are found for the Easterlin paradox and the Kuznets consumption puzzle and it is concluded that rank concerns tend to strengthen the case for more income equality and weaken the standard effect of inequality on aggregate saving.