Ottman et al. (2001) grew sorghum plants in a FACE experiment conducted near Phoenix, Arizona, USA, where plants were fumigated with air containing either 360 or 560 ppm CO2 and where they were further subjected to irrigation regimes resulting in both adequate and inadequate levels of soil moisture.  Averaged over the two years of their study, the extra CO2 increased grain yield by only 4% in the plots receiving adequate levels of soil moisture but by fully 16% in the dry soil moisture plots.

Prior et al. (2005) grew sorghum in two different years in 7-meter-wide x 76-meter-long x 2-m-deep bins filled with a silt loam soil, upon which they constructed a number of clear-plastic-wall open-top chambers they maintained at ambient CO2 concentrations and ambient concentrations plus 300 ppm.  In the first of the two years, the extra CO2 increased sorghum residue production by 14%, while in the second year it increased crop residue production by 24% and grain production by 22%.  For a CO2 increase of 200 ppm comparable to that employed in the study of Ottman et al., these figures translate to crop residue increases of 9% and 16% and a grain increase of 15%.

In a review of primary research papers describing results obtained from large-scale FACE experiments conducted over the prior fifteen years, Ainsworth and Long (2005) determined that, in the mean, sorghum grain yield was increased by approximately 7% in response to a 200-ppm increase in the atmosphere's CO2 concentration.

An experiment with a bit more complexity was carried out several years earlier by Watling and Press (1997), who grew sorghum with and without infection by the parasitic C3 weeds Striga hermonthica and S. asiatica.  The study lasted for about two months and was conducted in controlled environment cabinets fumigated with air of either 350 or 700 ppm CO2.  In the absence of parasite infection, the extra 350 ppm of CO2 boosted plant biomass production by 35%, which adjusted downward to make it compatible with the 200-ppm increase employed in most FACE studies corresponds to an increase of just under 21%.  When infected with S. asiatica, the biomass stimulation provided by the extra CO2 was about the same; but when infected with S. hermonthica, it was almost 80%, which corresponds to a similarly downward adjusted biomass increase of 45%.

In light of these several observations, it would appear that although the CO2-induced increase in total biomass and grain yield of sorghum is rather modest, ranging from 4 to 16% under well-watered conditions, it can be on the high end of this range when the plants are stressed by a shortage of water (16% has been observed) and by parasitic infection (45% has been observed).  Consequently, elevated levels of atmospheric CO2 seem to help sorghum most when help is most needed.

References
Ainsworth, E.A. and Long, S.P.  2005.  What have we learned from 15 years of free-air CO2 enrichment (FACE)? A meta-analytic review of the responses of photosynthesis, canopy properties and plant production to rising CO2.  New Phytologist 165: 351-372.

Ottman, M.J., Kimball, B.A., Pinter Jr., P.J., Wall, G.W., Vanderlip, R.L., Leavitt, S.W., LaMorte, R.L., Matthias, A.D. and Brooks, T.J.  2001.  Elevated CO2 increases sorghum biomass under drought conditions.  New Phytologist 150: 261-273.

Prior, S.A., Runion, G.B., Rogers, H.H., Torbert, H.A. and Reeves, D.W.  2005.  Elevated atmospheric CO2 effects on biomass production and soil carbon in conventional and conservation cropping systems.  Global Change Biology 11: 657-665.

Watling, J.R. and Press, M.C.  1997.  How is the relationship between the C4 cereal Sorghum bicolor and the C3 root hemi-parasites Striga hermonthica and Striga asiatica affected by elevated CO2?  Plant, Cell and Environment 20: 1292-1300.