Photosynthesis in $\mathrm{C}_4$ plants is relatively less limited by atmospheric $\mathrm{CO}_2$ levels…
Photosynthesis in $\mathrm{C}_4$ plants is relatively less limited by atmospheric $\mathrm{CO}_2$ levels because:
effective pumping of $\mathrm{CO}_2$ into bundle sheath cells
rubisco in $\mathrm{C}_4$ plants has higher affinity, for $\mathrm{CO}_2$
four carbon acids has the primary initial $\mathrm{CO}_2$ fixation products
the primary fixation of $\mathrm{CO}_2$ is mediated via PEP carboxylase.
Solution
In $\mathrm{C}_4$ plants, initial fixation of carbon dioxide occurs in mesophyll cells. The primary acceptor of $\mathrm{CO}_2$ is phosphoenol pyruvate or PEP. It combines with carbon dioxide in the presence of PEP carboxylase or PEPcase to form oxaloacetate. $\mathrm{C}_4$ plants are more efficient in picking up $\mathrm{CO}_2$ even when it is found in low concentration because of the high affinity of PEPcase.
Related Theory
The two key restrictions slow down photosynthesis in $C_3$ cycle:
(i) Rubisco aims to fix carbon dioxide, but can also fix oxygen molecules, which creates a toxic two-carbon compound. Rubisco fixes oxygen about 20 percent of the time, initiating a process called photorespiration that recycles the toxic compound. Photorespiration costs the plant energy it could have used to photosynthesize.
(ii) When stomata are open to let carbon dioxide in, they also let water vapor out, leaving $\mathrm{C}_3$ plants at a disadvantage in drought and high-temperature environments.