Continuous and Discontinuous Response to Smoothly Decreasing Effective Distance: An Analysis with Special Reference to ‘Overbanking’ in the 1920s

An important problem of general interest concerns the aggregate response of a system to increasing density (or decreasing effective distance between units). An analysis is made for a system in which the individual responses to changing density are smooth. The analysis is presented in terms of the ‘overbanked’ situation of the USA in the 1920s. Models are derived from micro-economic principles concerning the interaction of two banks in competition for deposits as road transportation decreases in relative cost. The conclusion drawn from analysis of the models is that aggregate deposits may increase in a smooth or in a discontinuous (jump) fashion, the jump depending on the nature of an individual banker's response function and occurring despite smooth individual responses. In the case where the system is always in equilibrium, the jump may be a catastrophe in the sense described by Thorn. The analysis indicates that improvements in road transportation may have significantly reduced the stability of the banking system to a point of catastrophic collapse (as well as, for example, overzealous chartering by the authorities). The analysis should have application to many other situations in which decreasing effective distance is an important fact.