Explanations of economic growth and prosperity commonly identify a unique causal effect, e.g., institutions, culture, human capital, geography. In this paper we provide instead a theoretical modeling of the interaction between culture and institutions and their effects on economic activity. We characterize conditions on the socio-economic environment such that culture and institutions complement (resp. substitute) each other, giving rise to a multiplier effect which amplifies (resp. dampens) their combined ability to spur economic activity. We show how the joint dynamics of culture and institutions may display interesting non-ergodic behavior, hysteresis, oscillations, and comparative dynamics. Finally, in specific example societies, we study how culture and institutions interact to determine the sustainability of extractive societies as well as the formation of civic capital and of legal systems protecting property rights.