In a previous paper (Winter et al., 1990) we demonstrated the existence of a new type of auditory-nerve rate-intensity function, the straight type, as well as a correlation between rate-level type, threshold and spontaneous rate. In this paper we now show that the variation in rate-intensity functions has its origin in the basilar membrane nonlinearity. Comparison of rate-intensity functions at characteristic frequency and at a tail-frequency show that the rate-intensity functions are identical at low firing rates and that the sloping-saturation and straight types deviate from the standard function only at higher firing rates. The frequencies at which the deviations occur, and the change from saturating to sloping-saturation or straight, are closely correlated with the characteristic frequency of the fibre. Using the tail-frequency rate-intensity function as a calibration, it is possible to derive the basilar membrane input-output function at characteristic frequency from the characteristic frequency rate-intensity function. The resulting derived basilar membrane input-output functions are of a simple form and agree well with published direct measurements of basilar membrane motion. They show that the wide dynamic range to which the cochlea responds, about 120 decibels, is compressed by the basilar membrane nonlinearity into a much smaller range of about 30-35 decibels. General characteristics of the derived basilar membrane input-output curves show features which agree well with psychoacoustic studies of loudness estimation.