Are employment policies counterproductive when wage setting is centralised?

When government policy is subjected to a balanced budget constraint or a current account constraint, total income of the workers is independent of the employment policy. An employment policy distributes income more evenly, and may lead to a union with strong preferences for equality to raise its wage. However, a sufficiently vigorous employment policy is always effective. Unions which maximise the after tax real wage is always lower the nominal wage when government employment policy becomes more vigorous. The constraints enforce an implicit tax-based incomes policy (TIP), and there is limited scope due to centralisation for other forms of TIP.