The LQI has been used to determine an acceptable level of expenditure that can be justifiably incurred on behalf of the public interest in exchange for a small reduction in the risk of death that results in improved life-quality for all. This limit of benefit can be considered as the societal capacity to commit resources to sustainable risk reduction. Suppose a portion of GDP, dG, is invested in implementing a program that affects public risk, thus modifying the life expectancy by a small amount dE. There is a net benefit if there is a net increase in LQI, dL. This criterion can be derived from the definition of L as: