OPTIMISING ANTI-POVERTY TRANSFERS WITH QUANTILE ... - Ivie

10
Z b
a
k(y)dF (y),
where a is the lower bound of integration, b is the upper bound, k is a derivable
kernel function and F is the cdf of the living standards y.
The optimisation
program is
max
t(y)
Z b
−
a
k(y + t(y))dF (y)
subject to:
Z b
a
t(y)dF (y) =B and t(y) ≥ 0, for all y,
Assume that the transfer function is continuously differentiable. The corresponding
Euler necessary condition can be calculated. A convexity condition involving
on the kernel function and function t(.) can make the Euler conditions
sufficient.
Typically, kernel function k is differentiable in the classical calculus of variations,
which implies that it must be continuous. In the case of a poverty index, the
kernel is the product of a function P (y, z) and the dummy for the poor 1 [y+t(y)