  We calculate the effective resistivity of a macroscopically disordered two
dimensional conductor consisting of two components in a perpendicular magnetic
field. When two components have equal area fractions, we use a duality theorem
to show that the magnetoresistance is non-saturating and at high fields varies
exactly linearly with magnetic field. At other compositions, an effective
medium calculation leads to a saturating magnetoresistance. We briefly discuss
possible connections between these results and magnetoresistance measurements
on heavily disordered chalconide semiconductors.
