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In this paper we address the joint distribution and growth processes by combining the inherent conservative property of distributions, highlighted by the mean-field game liter- ature, and simple capital accumulation dynamics of benchmark economic growth theory. Given an initial unequal distribution of capital, and assuming a deterministic setting, we show that there are three main types of evolutions: asymptotic equality but no long run growth, asymptotic growth and a stationary distribution featuring inequality, or growth together with increasing inequality. The last type of evolution is Pareto optimal if capital accumulation depends linearly on the capital stock. Introducing a multiplicative random capital redistribution process, we show that we always get an increase in inequality al- though it can occur together with growth (if noise is relatively low) or within a non-growth context (when noise is very high).
