A Dichotomous Analysis of Unemployment Welfare

In an economy which could not accommodate the full employment of its labor force, it employs some labor but does not employ others. The bipartition of the labor force is random, and we characterize it by an axiom of equal employment opportunity. We value each employed individual by his or her marginal contribution to the production function; we also value each unemployed individual by the potential marginal contribution the person would make if the market hired the individual. We then use the aggregate individual value to distribute the net production to the unemployment welfare and the employment benefits. Using real-time balanced-budget rule as a constraint and policy stability as an objective, we derive a scientific formula which describes a fair, debt-free, and asymptotic risk-free tax rate for any given unemployment rate and national spending level. The tax rate minimizes the asymptotic mean, variance, semi-variance, and mean absolute deviation of the underlying posterior unemployment rate. The allocation rule stimulates employment and boosts productivity. Under some symmetry assumptions, we even find that an unemployed person should enjoy equivalent employment benefits, and the tax rate goes with this welfare equality. The tool employed is the cooperative game theory in which we assume many players. The players are randomly bipartitioned, and the payoff varies with the partition. One could apply the fair distribution rule and valuation approach to other profit-sharing or cost-sharing situations with these characteristics. This framework is open to alternative identification strategies and other forms of equal opportunity axiom.