Simple biomass production models are used to assess crop productivity under a wide range of environmental conditions, typically as a component of crop growth models. Two simple biomass production models are widely used, one based on radiation-use efficiency, e (B=e St fi), and the other on water-use efficiency, w (B=w T=K T/Da), where B is biomass, St is incoming solar radiation, fi is the fraction of incoming solar radiation intercepted by the canopy, T is transpiration, and K is transpiration to biomass coefficient, which divided by the air vapor pressure deficit (Da), allows estimating w. The expectation is that normalization by Da would account for the effects of climate variations on w, while would be reasonably constant across diverse environment. The usefulness of these models depends on how conservative e or K are across locations or as weather changes throughout the crop growing season. However, the evaluation of the transferability of these parameters is not simple due to the scarcity of experimental values and the lack of methodological consistency. For this reason we developed and tested a mechanistic canopy transpiration and photosynthesis model, and we use it to obtain simulated values of e, w, and K for maize and wheat in eight world locations with diverse weather. Results showed that e is not conservative but fluctuates significantly, although variations correlate well with Da, St, and the diffuse fraction of St. However, temperature outside the optimum range for photosynthesis appeared to be a factor of fluctuation needing more attention. Water-use efficiency was less affected by temperatures because both photosynthesis and transpiration are either reduced or increased. Results showed that K is not a constant, but rather a function of the internal (sub-stomatal cavity) to atmospheric CO2 concentration ratio, which is not constant as usually assumed and seems to depend on Da.