  We study the equilibria of a photoresponsive nematic elastomer ribbon within
a continuum theory that builds upon the statistical mechanics model put forward
by Corbett and Warner [Phys. Rev. E 78, 061701 (2008)]. We prove that the
spontaneous deformation induced by illumination is not monotonically dependent
on the intensity $I$. The ribbon's deflection first increases with increasing
$I$, as expected, but then decreases and abruptly ceases altogether at a
critical value $I_\mathrm{e}$ of $I$. $I_\mathrm{e}$, which is enclosed within
a hysteresis loop, marks a first-order shape transition. Finally, we find that
there is a critical value of the ribbon's length, depending only on the degree
of cross-linking in the material, below which no deflection can be induced in
the ribbon, no matter how intense is the light shone on it.
