  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.
