  Two very different methods -- exact diagonalization on finite chains and a
variational method -- are used to study the possibility of a metal-insulator
transition in the symmetric half-filled periodic Anderson-Hubbard model. With
this aim we calculate the density of doubly occupied $d$ sites as a function of
various parameters. In the absence of on-site Coulomb interaction ($U_f$)
between $f$ electrons, the two methods yield similar results. The double
occupancy of $d$ levels remains always finite just as in the one-dimensional
Hubbard model. Exact diagonalization on finite chains gives the same result for
finite $U_f$, while the Gutzwiller method leads to a Brinkman-Rice transition
at a critical value ($U_d^c$), which depends on $U_f$ and $V$.
