Part 2 extends the analysis to show that it is possible to find the "permission point", the value of (the coefficient of relative) risk-aversion, at which decisions to sanction environmental protection are most likely to be made. The mathematical model describes the process by which the decision maker varies his risk-aversion over a range of feasible values to find the risk-aversion that will give him the greatest desire to invest in the protection system under consideration. If he can find such a risk-aversion before losing discrimination (because the system is too expensive, given its performance), he will adopt it as his "permission point" and decide in favour of the expenditure. The permission point is, of course, bounded above by the point of indiscriminate decision. A maximum Risk Multiplier calculated at the point of indiscriminate decision may be applied to the protection expenditure at monetary break-even to give the maximum, rational outlay on protection. Moreover, it is possible to model how the average UK adult should take decisions on protection to maximise his utility. Different situations will call for different values of risk-aversion, which may explain why economists have come up with differing estimates of this parameter in the past. However, a central, average risk-aversion may be calculated for the average UK adult as 0.85, which is within 4% of the value, 0.82, found from the newly reported method based on a trade-off between income and future free time, and is consistent with several recent economic estimates. Worked examples assess how much an organisation should spend on a protection scheme to prevent accidents with very large environmental consequences. (C) 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.