Optimal Redundancy Compensation

Abstract

The potential welfare gain arising from a redundancy is the increase in the value of output as the worker is compelled to change jobs. The Redundancy Payments Act scheme is an example of a compensation mechanism whereby the gainers compensate the losers. The evidence of Daniel (1974) suggests that the scheme is inadequate, and Pengilly (1975) proposed an alternative income-maintenance scheme. Both schemes, like the one considered below, consist of a lump-sum payment, plus a time-path of earnings-related unemployment pay. We define an optimal compensation scheme as one that maintains the expected lifetime utility of a worker at the level he would have enjoyed without redundancy, at the lowest expected cost. A worker's expected lifetime utility may fall when he loses his job because of an increase in risk as well as a lower present value of future earnings. Offset against this may be change in the expected amount of leisure. The cost of the scheme equals the lump-sum payment, plus the expected value of unemployment pay over his working lifetime, less the expected value of income-tax payments by the worker. These expectations depend on the probability that a worker will be employed at each subsequent time, and the expected value of his wage at each time. These in turn depend on the frequency distribution of wage offers open to the worker, and the time-path of his acceptance wage. Unemployment pay may be a cheaper method of maintaining expected lifetime utility because it will be paid as, and when, his income without compensation is lower. A lump-sum payment, by increasing the probability that the worker will be in a job at each subsequent time, may reduce the expected value of unemployment pay and increase the expected value of tax receipts. We find that unemployment pay should be positive, but fall over time. A lump-sum payment in addition will be optimal if the wage currently earned by the worker is so high that the probability of his obtaining a job at a very much higher wage is low, and if the income-tax rate is high.