m ∈ [m(n), τrt(n)], where this interval may vary by skill type. Taking the tax-transfer into
account, a worker experiences utility level u(c(n), m), where the function u is increasing
in its first argument, decreasing in its second argument, continuously differentiable and
strictly concave. Someone outside the labor market experiences utility u(b, r), where the
workfare variable r measures some combination of the duration, intensity, and unpleas-
antness of the required activity. In this basic version of the model, we assume that all
individuals find workfare equally onerous; in other words, r is the same for everyone. We
assume that r is measured in such a way that r = 0 when there are no work requirements.
Under these conditions, individuals differ along two dimensions and can be characterized
by an ordered pair (m, n). The population is described by a continuous distribution
function F(m,n) with a density f (m, n) with support [m(n),m(n)] × [n, n].
Given the policies adopted by the government, individuals decide whether to work or
not. An individual works if
u(c(n), m) ≥ u(b, r). (1)
For each n, those individuals with the lowest values of m choose to work, while those
with a relatively higher preference for leisure remain outside the labor force. Indeed, for
each n, there exists a critical value m*(c(n), b, r) such that the workers with skill type n
are exactly those that have m < m*(c(n),b,r). This critical value is determined by the
equation
u(c(n), m*(c(n), b, r)) = u(b,r). (2)
It follows immediately from the properties of the utility function that m*(c(n),b,r) —
and, consequently the size of the workforce — increases when c(n) or r increases or when
b decreases. The greater is after-tax income from employment, the more desirable is
work. The more unpleasant the workfare activity, the less desirable is being out-of-work.
In either case, the relative return to working increases, thereby encouraging labor market
participation. The greater is the public welfare benefit, the more desirable is remaining
out of the labor market, so participation falls. We assume that m*(c(n),b,r) ∈ (m,m)
for all skill types n, so that small changes in program parameters always have some effect