  We use an abelian model to study linear power corrections which arise from
infrared renormalons and affect event shapes in $e^+e^-$ annihilation into
hadrons. While previous studies explored power corrections in the two-jet
region, in this paper we focus on the three-jet region, which is the most
relevant one for the determination of the strong coupling constant. We show
that for a broad class of shape variables, linear power corrections can be
written in a factorised form, that involves an analytically-calculable
function, that characterises changes in the shape variable when a soft parton
is emitted, and a constant universal factor. This universal factor is
proportional to the so-called Milan factor, introduced in earlier literature to
describe linear power corrections in the two-jet region. We find that the power
corrections in the two-jet and in the three-jet regions are different, a result
which is bound to have important consequences for the determination of the
strong coupling constant from event shapes. As a further illustration of the
power of the approach developed in this paper, we provide explicit analytic
expressions for the leading power corrections to the $C$-parameter and the
thrust distributions in the $N$-jet region for arbitrary $N$, albeit in the
abelian model.
