Private and Social Welfare Gains in the Diamond‐Dybvig Model: A Rationale for the Existence of Banks

In this paper, I evaluate the private and the social welfare gains that in the Diamond-Dybvig model of bank runs characterise the switch from a decentralised to a centralised equilibrium that may hold even in an atomistic environment with banking intermediation. Relying on logarithmic preferences, I show that such a social welfare gain is an increasing function of the discount rate of more patient agents. Moreover, I demonstrate that for each level of the discount rate of agents who are willing to postpone consumption, there is an optimal value of the proportion of these agents in the economy that maximises the social welfare gain.