To see the role of ongoing lending in our results so far, recall that constraint 5 on the social planning problem specifically allowed it to borrow in period 1 (up to the credit ceiling minus period 0 borrowing, / — d) to finance the withdrawals of impatient agents. In addition, we assumed that these additional period 1 loans would be extended even in the event that a run occurred that period. This is evident in the fact that run condition 15 allows the bank to liquidate capital all the way to the maximum level Z+, which includes the repayment of period 1 debt b (see equation 14). For future reference, notice that 15 can be re-written as
Hence, the run condition 19 is more stringent than 17, so the bank is more vulnerable to runs if foreign creditors fail to engage in ongoing lending in the event of a run. The intuition is, clearly, that the inability to borrow b as planned reduces the liquid resources that the bank has access to in the event of a run.
Would it be rational for foreign lenders not to engage in ongoing lending? Suppose that 22 holds and that foreign lenders are “small.” If every foreign creditor refuses to lend to the bank and depositors panic, the bank will have to liquidate all of the long term asset, except what is necessary to repay initial debt d in period 2 -and any debt above and beyond d could not be repaid then. Hence no individual creditor will find it profitable to lend to the bank in period 1.
This has the striking implication that the behavior of international lenders may, by itself, cause a depositors’ run: if parameters are such that 22 holds but 21 does not, a run on deposits is possible if and only if external creditors refuse to extend additional loans in period 1. In such case, creditors may stop lending because they fear that a bank run will occur, which makes the bank run possible. By withholding additional funds the creditors may provoke a crisis, and by providing them they may avoid it.
There are two caveats to this argument. The first is that we have assumed that the bank waits until period 1 to borrow the resources necessary to finance the withdrawals of impatient depositors. An alternative strategy would have the bank borrow the full / dollars in period 0, to be repaid in period 2. At the same time, it would buy b dollars of the liquid asset, which in real-world parlance corresponds to having b dollars of “reserves” deposited in liquid form abroad. In period 1 it would use the b dollars to finance the consumption of impatient depositors, and hence it would not be vulnerable to confidence crisis by creditors. But in practice, this alternative strategy may not be feasible. Foreign lenders may not be willing to disburse the full / at first, especially if a portion is to be used for consumption, not investment. Moreover, the borrowing rate at which the bank could get the / dollars abroad is likely to be much higher than the deposit rate at which it could keep the b dollars in liquid form; this interest rate wedge could render this scheme’s cost prohibitive. Electronic Payday Loans Online