We can now discuss the outcomes of a demand deposit system. A first result is that demand deposits may implement the social optimum. This is because this game has an honest equilibrium in which each agent withdrawal decision corresponds to her true type: in period 1 only impatient deposit tors retire x pesos, the bank does not fail, and pays у to patient depositors in period 2. Verifying that honest behavior is an equilibrium entails only checking that honesty is consistent with the bank’s solvency (which is true by construction) and that each depositor finds it optimal to tell the truth about her type (which is easy and left to the reader).
This result clarifies the role of a demand deposit system in an open economy. Banks may implement a socially optimal allocation that, in particular, improves upon what agents can achieve in isolation.
However, the banking system may attain such improvement only by holding less internationally liquid assets than its implicit liabilities. Consequently, the banking system may be subject to a run. In particular, it can happen that all domestic agents decide to attempt to withdraw their deposits in period 1 they expect all others to do the same. Such collective behavior turns out to be individually optimal, as it can be easily checked, if it forces the bank to run out of resources and fail before it can meet all the claims made on it.
Now, if all agents attempt to withdraw their deposits in period 1, the bank will fail if
assumption. Only if a < 1 can runs be ruled out. Hence, while runs may or may not occur, the run condition is satisfied for many plausible parameter values of the utility and production technologies. Electronic Payday Loans Online