Limited memory and the essentiality of money

This paper investigates the relationship between memory and the essentiality of money. We consider a random matching economy with a large finite population in which commitment is not possible and memory is limited in the sense that only a fraction m E(0; 1) of the population has publicly observable histories. We show that no matter how limited memory is, there exists a social norm that achieves the first best regardless of the population size. In other words, money can fail to be essential irrespective of the amount of memory in the economy. This suggests that the emphasis on limited memory as a fundamental friction for money to be essential deserves a deeper examination.