Empirical literature predicts a non-monotonic relationship between corruption and economic growth. In this paper we provide a theoretical framework that can explain this non-monotonicity in terms of a dynamic interaction between culture and corruption. In a heterogenous agent framework, we show that presence of agents with high moral values and a cultural aversion towards corrupt practices helps in reducing the overall degree of corruption. At the same time, for any given level of corruption, high moral agents are less adaptable to game an already corrupt system in pursuit of economic profits. Thus the initial cultural composition of the population interacts with economic incentives to generate differential growth paths for different economies. Moreover, the cultural composition of the population changes endogenously responding to economic growth, which creates possibilities of multiple balanced growth paths and culture-induced poverty traps.