  Inclusive single pion photoproduction on the deuteron is studied in the first
resonance region. The calculation is based on the use of the diagrammatic
approach. Pole diagrams and one-loop diagrams with NN rescattering in the final
state are taken into account. The elementary operator for pion photoproduction
from the nucleon is taken in on-shell form and calculated using the SAID and
MAID multipole analyses. Our predictions for total and differential cross
section show good agreement with the available experimental data. Invoking some
information on the reactions $gamma d\to\pi^0 d and $\gamma d\to np$ we predict
the total photoabsorption cross section for deuterium. We find that our results
overestimate the experimental data in the center of the \Delta-peak (\sim 320
MeV) by about 10%.
