Loudness matching functions for tones for persons with one shifted- threshold ear (hearing loss and noise-shifted thresholds) and one ear within normal limits were used to derive the presumed basilar membrane (BM) input- output (I/O) function in a normal ear. The comparison was made by assuming that the BM I/O function for the ear with the cochlear threshold shift has a slope of one (a linearized cochlea). The function for the normal ear was derived from the loudness matching function based on this assumption. Comparisons were made for archival basilar membrane data [M. A. Ruggero, N. C. Rich, A. Recio, S. S. Narayan, and L. Robles, J. Acoust. Soc. Am. 101, 2151-2163 (1997)] for chinchilla and archival loudness matches for long- duration tones for persons with various degrees of cochlear hearing loss [F. Miskolczy-Fodor, J. Acoust. Soc. Am. 32, 486492 (1960)]. Comparisons were made also between BM I/O functions and ones derived from loudness matches for persons with unilateral hearing loss simulated by broadband noise. The results show a close resemblance between the basilar membrane I/O function and the function derived from loudness matches for long-duration tones, even though the comparison was between human and chinchilla data. As the degree of threshold shift increases from 40 to 80 dB, the derived BM I/O functions become shallower, with slopes for losses of 60 dB or more falling in the range of values reported for physiological data. Additional measures with short-duration tones in noise show that the slope of the loudness function and the slope of the derived basilar membrane I/O function are associated with the behavioral threshold for the tone. The results for long-duration tones suggest a correspondence between BM displacement and loudness perception in cases of recruitment, but the relation between the degree of loss and the amount of BM compression and the relation between signal duration and compression suggests that other factors, such as the neural population response, may play a role.