  We present a simple, semianalytical approach to compute the line emission of
C+, C and CO in Photodissociation Regions of varying metallicity that depends
on very few parameters and naturally incorporates the clumpiness of the
interstellar medium into the calculations. We use it to study the dependence of
the I_[C II]/I_CO and I_[C I]/I_CO line ratios on the metallicity. We show how
to modify it to include the effects of density and radiation field, and we have
compared it with observational data. We find that the model explains the
observed trend of enhanced [C II]/CO line ratio with decreasing metallicity as
the natural result of the augmented fraction of photodissociated gas in a
clump. We show that enhanced [C II]/CO ratios can be produced by lowering the
upper limit of the clump size distribution, as may happen in 30 Doradus. We
also find that the available data favors a [C I]/CO intensity ratio essentially
independent of metallicity, albeit the paucity of observations does not exclude
other possibilities. This is difficult to understand if most of the C is
produced by UV photons as is the case with C+. Finally, we study the prediction
of the model for the trend of the X_CO factor with metallicity. Comparison with
previous observational studies yields good agreement.
