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We investigate the relation between money and memory in computational systems. To do so, we introduce a model in which agents have a state associated with them that is known to those interacting with them. The joint states of agents who interact successfully change according to some prescribed probability distribution. We show that such mechanisms can in fact encode and generalize a rich variety of monetary mechanisms, while requiring very little memory per agent to represent state, possibly even a single bit. We explore how monetary considerations like the total amount of money apply in our model, and seek memory-based mechanisms that increase social welfare. We examine the natural encoding of a token-based system in memory, in which tokens are exchanged and conserved during each transaction. We find that mechanisms that use price discrimination or do not conserve tokens can provide higher social welfare.