Climate models generally simulate a unidirectional, positive liquid water path (LWP) response to increasing aerosol number concentration. However, satellite observations and large‐eddy simulations show that the LWP may either increase or decrease with increasing aerosol concentration, influencing the overall magnitude of the aerosol indirect effect (AIE). We use large‐eddy simulation to investigate the LWP response of a marine stratocumulus cloud and its dependence on different parameterizations for obtaining cloud droplet number concentration (CDNC). The simulations confirm that the LWP response is not always positive—regardless of CDNC treatment. However, the AIE simulated with the model version with prescribed CDNC is almost 3 times larger compared to the version with prognostic CDNC. The reason is that the CDNC in the prognostic scheme varies in time due to supersaturation fluctuations, collection, and other microphysical processes. A substantial spread in simulated AIE may thus arise simply due to the CDNC treatment. Plain Language Summary Our poor understanding of aerosol‐cloud‐radiation interactions (aerosol indirect effects) results in a major uncertainty in estimates of anthropogenic aerosol forcing. In climate models, the cloud water response to an increased aerosol number concentration may be especially uncertain as models simplify, or do not account for, processes that affect the cloud droplet number concentration and the total amount of cloud water. In this study, we employ large‐eddy simulation to explore how different model descriptions for obtaining the number concentration of cloud droplets influences the cloud water response of a marine stratocumulus cloud and thus the simulated aerosol indirect effect. Our simulations show a qualitatively similar cloud water response regardless of model description: the total amount of cloud water increases first and then decreases with increasing aerosol concentration. However, the simulated aerosol indirect effect is almost 3 times as large when the number concentration of cloud droplets is prescribed compared to when it is dependent on the calculated supersaturation and other microphysical processes such as collisions between cloud droplets. Our findings show that a relatively simple difference in the treatment of the number concentration of cloud droplets in climate models may result in a significant spread in the simulated aerosol indirect effect. Key Points We use large‐eddy simulation to investigate the response of a marine stratocumulus cloud to increasing aerosol concentration The aerosol indirect effect is almost 3 times as large when the cloud droplet concentration is prescribed instead of prognostic Time variations in supersaturation and collection influence the overall cloud droplet number and aerosol indirect effect