How will increased $\ce{CO2}$ affect forests and other vegetative areas?
If you increase CO2 concentration and keep all other parameters at there current level, then biomass production should go up. The reason is simply that CO2 is one of the building blocks biomass is made of in photosynthesis.

In the real world it's trickier than that of course. Here you have to take into account how natural cycles will be affected by increased CO2 levels. Temperatures e.g. will go up which is expected to be beneficial for biomass production for moderate increases and becomes increasingly bad for higher increases. Precipitation patterns change, wind patterns and therefore soil erosion change etc. etc.

Chapter 7 of the IPCC report deals with the question how climate change affects biogeochemical cycles; biomass production is one of the parameters that go into the carbon cycle.

To my knowledge biomass production is one of the parameters that benefit from moderate temperature increase but are expected to turn to their opposite around the 2-degree benchmark.