  We analyze the dc Josephson effect in a ballistic
superconductor/ferromagnet/superconductor junction by means of the
Bogoliubov-de Gennes equations in the quasiclassical Andreev approximation. We
consider the possibility of ferromagnetism originating from a mass
renormalization of carriers of opposite spin, i.e. a spin bandwidth asymmetry.
We provide a general formula for Andreev levels which is valid for arbitrary
interface transparency, exchange interaction, and bandwidth asymmetry. We
analyze the current-phase relation, the critical current, and the free energy
in the short junction regime. We demonstrate that a larger number of $0-\pi$
transitions caused by a change in junction width or polarization magnitude is
expected when ferromagnetism is driven by spin bandwidth asymmetry compared to
Stoner magnetism, and that the same mechanism is likely responsible for the
flowing of a larger critical current. We compare the phase diagrams of two
identical junctions differing only in the mechanism by which the mid layer
becomes magnetic, i.e. Stoner magnetism or bandwidth asymmetry. In particular,
we point out that for these two cases, the phase difference across the junction
in the ground state need not be the same, even if the polarizations are equal.
