Workforce or Workfare?

When τ (n) is negative, employment of individuals of type n is subsidized by the tax
system. Such a subsidy is commonly referred to as an earned income tax credit (EITC).
When the net tax on employment is positive, it is common to refer to the tax system
as a negative income tax (NIT) scheme. Additionally, we denote by g (n) the (average
and endogenous) marginal social welfare weight given to workers of skill n, expressed in
terms of public funds. Formally,

m* (c(n) ,b,r)

g (n) ≡____1____ f ^du(c(n) ,m) f (_mn) dm             (6)

g ⁽n) ≡ λF (m∙,n) J ∂c (n) f ^(m,n) dm             (6)

m(n)

where λ is the Lagrange multiplier of the budget constraint (4).

Proposition 1 (Saez, 2002). The optimal participation tax for individuals of skill type
n is negative exactly when

g (n) > 1.                                           (7)

The condition governing optimality of an EITC scheme relates the average marginal
social welfare weight of workers of skill n (expressed in public funds) to one. This welfare
weight represents the dollar equivalent value for the government of distributing an extra
dollar uniformly to workers of type n. When this value is larger (lower) than one, then
these workers should receive a subsidy (should pay taxes) τ (n) < 0(> 0). The intensity of
required work might influence this condition through the cross-derivatives of the function
u (see (6)). If the marginal utility of consumption increases as workfare becomes more
intense, there is an increasing tendency for the inequality in (7), thereby moving the
optimal tax-transfer scheme in the direction of an EITC. However, given the focus of
the second step of our analysis, which is to examine the advisability of adding a small
workfare requirement, we will carry out our subsequent analysis under the assumption
that r = 0. By so doing, we can treat the issue of whether there is an EITC or an NIT
as fixed by the optimum without workfare.

We are now in a position to carry out the second step of our analysis. Imagine that the
government has solved the optimal-tax transfer problem associated without workfare. In

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