Using the GECROS model, we simulated the effect of improvements in photosynthesis a range of growth parameters, including yield, and on the εc (the conversion efficiency of absorbed solar energy to the chemical energy of biomass) and εi (the efficiency of solar energy interception or absorption by the canopy) parameters of the Monteith crop growth equation, for wheat and potato (which use C3 photosynthesis) and maize (which uses C4 photosynthesis). In the case of the C3 crops, the improvements in photosynthesis were via 20% increases in the parameters Vcmax (carboxylation capacity of Rubisco), Jmax (electron transport capacity), Sc/o (Rubisco specificity), κ2LL (efficiency of converting incident light into electron transport) and gm (mesophyll conductance), while for the C4 crop, it was via 20% increase in Vcmax, Jmax and Sc/o and a 20% decrease in gbs (the conductance that controls the leak of CO2 from the bundle sheath cells in C4 leaves). The changes were applied individually and in combination. The responses were modelled using climate data collected over a 10‐year period from 66 sites around Europe. Improvements in photosynthesis did result in increases in yield but with considerable variation between the parameters that were adjusted. The greatest increases were obtained for increases in Jmax and κ2LL (up to an average 11% increase for total plant biomass), and these increases were found across all Europe. Increases in both these parameters have a predominant effect on the light‐use efficiency for subsaturating irradiances. Improvements in the other parameters produced smaller increases.