Workforce or Workfare?

the notation of this article, it has found the optimal solution with the added constraint
that r = 0. Using the Envelope Theorem, the impact of a marginal increase in the
intensity of workfare on social welfare can be written

dW ∂u(b, 0) r f^m(ⁿ)     ʃ. .          .1 . .0m*(c(n),b, 0)_x, , ,j ,_o,

=— = —  J J       f(m,n)dmdn + λJ τ(n)-----------f(m,n)dn. (8)

The first term in (8) is negative, and it captures the welfare loss due to the disutility of
work felt by those engaged in the required work. The second term captures the effect of

workfare on the public budget. An increase in the intensity of required work increases
workforce by the net tax on working for that type τ (n) gives the change in tax revenue
received from workers of skill type n. Integrating over all skill types provides the total
effect on the public budget. If skill type n receives a participation subsidy then this
revenue effect is negative. In this event workfare induces more people to enter the labor
force, which increases the amount of public funds needed to finance the EITC scheme.

This discussion is summarized in Proposition 2.

Proposition 2. The introduction of a workfare program at low intensity reduces social
welfare if marginal participants receive, on average, a participation subsidy.

Proposition 2 is robust to some of the types of modifications to the government
objective functions often found in the literature. For example, the income maintenance
approach to workfare in Besley and Coate (1992, 1995) and the reduction of poverty in
after-tax income approach to nonlinear income taxes found in Kanbur et al. (1994) both
put zero social weight on the disutility of labor. Using this class of welfare functions
would effectively eliminate the first term from (8), and we could replace the “if” in
Proposition 2 with the phrase “if and only if.” The sign of the first term in (8) might

⁴ To a first order, these marginal participants experience no change in utility when entering the
workforce because they were previously indifferent between working and remaining out of the labor
force.

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