From this point, the analysis of Section 2 carries forward, with slightly more cumber-
some notation. The utilitarian social welfare function can be written
W=
n`n k⅛ pi
nk m
'ψ(k,,r)
u(c(n), m)f (m, n,
mm
k)dm +
J φ(k,r)
u(b, kr)f (m, n, k)dm
dk dn.
(12)
The budget constraint is
Zn kk φφ{krr} p
[n - c(n)]f (m, n, k)dm -
mk
bf (m, n, k)dm dk dn = R.
φ(k,r)
(13)
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
dW
dr
∂u(b, 0) f fk Г f( „ .
—f--JJJ f (m,n, k)dmdk dn
(14)
+ 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