Satiation of need is generally ignored by growth theory. I study a model where consumers may be satiated in any given good but new goods may be introduced. A social planner will never elect a trajectory with long-run satiation. Instead, he will introduce enough new goods to avoid such a situation. In contrast, the decentralized equilibrium may involve long run satiation. This, despite that the social costs of innovation are second order compared to their social benefits. Multiple equilibria may arise: depending on expectations, the economy may then converge to a satiated steady state or a non satiated one. In the latter equilibrium, capital and the number of varieties are larger than in the former, while consumption of each good is lower. This multiplicity comes from the following strategic complementary: when people expect more varieties to be introduced in the future, this raises their marginal utility of future consumption, inducing them to save more. In turn, higher savings reduces interest rates, which boosts the rate of innovation. When TFP grows exogenously and labor supply is endogenized, the satiated equilibrium generically survives. For some parameter values, its growth rate is positive while labor supply declines over time to zero. Its growth rate is then lower than that of the non satiated equilibrium. Hence, the economy may either coordinate on a high leisure, low growth, satiated "leisure society" or a low leisure, high growth, non satiated "consumption society".