This paper has considered the sequence of optimal credit expansion decisions of a bank operating under the legal structure imposed by the Federal Reserve System. Two alternative structures are considered, one relating to the pre-September 1968 period and the other to the currently enforced one. Using dynamic programming techniques, a closed-form equation for the optimal credit expansion decision has been derived in each case. The optimal level of credit expansion has been shown to be a nonlinear function of the prevailing interest rate, the parameters of the distribution of reserve losses, and several parameters set by Federal Reserve policy. The presence of uncertainty in the model has been shown to have an indefinite effect; however, several policy parameters may be chosen so as either to restrict or to encourage expansion to levels below or above the simple certainty prediction. These results are intuitively in accord with those of general inventory studies.

The problem considered in this paper is the optimal expansion or contraction of credit by a single bank in response to a change in its reserve account. Such a change is usually not of an exogenous nature when the entire operations of the bank are considered. Quite often, the change in the reserve position comes as a result of the bank's decision to engage in securities transactions, thereby changing its mix of reserves and securities without affecting the total asset position of the bank. We do not consider the overall portfolio selection problem faced by the bank; we assume that changes in the reserve account from such decisions are exogenous to our models.