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For money to be essential, environments have been considered in which there is imperfect monitoring of past actions and in which it is difficult to coordinate among economic agents. This paper provides an environment in which there is no monitoring of past actions while coordination is difficult. In this environment, we show that the first best allocation is achieved without money, and hence, money is not essential. The implication is that, for money to be essential, no monitoring is not enough but coordination must also be free.

Monitoring and coordination for essentiality of money