The trade-offs embodied in J-value safety analysis

The paper presents a new derivation of the J-value method for assessing health and safety expenditure that highlights the fact that two trade-offs are involved. The trade-off between safety spend and the resulting improvement in life expectancy rests on a prior trade between free-time fraction and income, made at a societal level. It is suggested that each trade is a specific instance of a more general exchange between expected free-time and income, and that the terms of the trade-off are similar, so that the percentage increase in life expectancy has the same value as a similar percentage increase in total expected free-time. The theoretical framework suggests that the average person values all his time equally, but perceives that he has sold his expected working time to an employer, so that, while he will still place a value on it, he does not see that value as coming to him, but rather going to his employer in exchange for the compensation he is being paid. Thus he values the extra years of life expectancy he obtains from a health and safety measure solely in terms of the extra years of free-time he expects to gain. The value of the exponent in the life-quality index has been shown to be equal to both the modulus of the elasticity of expected future free-time with respect to income and the modulus of the elasticity of life expectancy with respect to income. The indifference curves on the planes of income versus life expectancy and income versus discounted life expectancy have been shown to be the loci of J = 1. The actuarial basis for the calculation of working time fraction to the end of life has been explained, and data on the share of wages in Gross Domestic Product have been discussed. Based on recent statistics from the UK economy, the average person would be prepared to forego about 5½% of his income to the end of life in order to increase his life expectancy or discounted life expectancy by 1%, and would require his lifetime income to be increased by 5½% to compensate him for a loss of 1% in his life expectancy, discounted or otherwise. A small degree of asymmetry will, however, occur for larger percentage changes in life expectancy, with the average person requiring somewhat more compensation for a loss of life expectancy than he is prepared to pay for a gain.