The J-value is an objective method for determining when life extending measures are sensible, applicable to both manufacturing and service industries, including public health and healthcare. A model of human decision making based on the J-value is able to explain the shape of the Preston curve that relates life expectancy at birth and gross domestic product (GDP) per head for all the nations in the world. Making a number of reasonable assumptions, a J-value model produces a population-average life expectancy, which may be translated easily into a corresponding life expectancy at birth when life expectancy is not modified by discounting (net discount rate equals zero). The resultant values may be tested against pan-national data, showing a very good match. Thus the shape of the Preston curve has been explained and, at the same time, validation has been provided for the J-value model. A perturbation analysis shows that the J-value explanation for the Preston curve starts to break down as the net discount rate is increased above zero. Thus the Preston curve may be seen to validate the J-value model at a net discount rate of zero, but not at higher net discount rates. The result allows a closed-form expression to be derived for the first time for the pure time discount rate, namely the product of the rate of economic growth and the complement of risk-aversion. A further conclusion from the work is that no discernable limit is apparent before the age of 100 to the process by which people live longer as they get richer; such an intrinsic limit might be overcome by future improved medical technology. (C) 2017 The Author(s). Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.