Workforce or Workfare?

From this point, the analysis of Section 2 carries forward, with slightly more cumber-
some notation. The utilitarian social welfare function can be written

The budget constraint is

Apart from the appearance of φ in place of m* and integration over the variable k,
equations (12) and (13) are identical to the corresponding equations (3) and (4) in Section
2. Starting from a optimal tax-transfer scheme with no workfare, the effect of a marginal
increase in r is

∂u(b, 0) f f^k Г _f(          „ .

—f--JJJ   f (m,n, k)dmdk dn

+ λ ʃ ʃ τ(n) ^∂ ,—f (ψ(k, 0),n)dmdkdn.

Equation (14) is a direct analogue of (8) and can be interpreted in exactly the same way.

Thus, Proposition 2 carries over in this extended version of the model.

3.2 Distaste for Workfare as a Function of the Other Characteristics

As a further test of the robustness of the basic model, we now consider an economy in
which the distaste for required work is a function of an individual’s other characteristics.
We return to a world in which individuals vary only with respect to m and n. The
utility of an individual on workfare is given by u(b, ψ(r, m, n)), where, as in the previous
subsection, r is some objective measure of required work. The function ψ is increasing
in r , but there are no a priori reasons to restrict how ψ varies with m and n. In this
framework, an individual is indifferent between market work and remaining out of the
labor force if

u(c(n), m) - u(b, ψ(r, m, n)) = 0.                          (15)

10

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