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
there is effective pumping of $\mathrm{CO}_2$ into bundle sheath cells
RuBisCO in $\mathrm{C}_4$ plants has higher affinity for $\mathrm{CO}_2$
six carbon acids are the primary initial $\mathrm{CO}_2$ fixation products
the primary fixation of $\mathrm{CO}_2$ is mediated via PEP carboxylase.
Solution
$\mathrm{CO}_2$ acceptor molecule in $\mathrm{C}_4$ plants is phosphoenol pyruvate (PEP). $\mathrm{C}_4$ plants are more efficient in picking up $\mathrm{CO}_2$ even when it is found in low concentration because of high affinity of PEP. PEP carboxylase (PEPcase) is the key enzyme which catalyses the primary fixation of $\mathrm{CO}_2$.