Chromonics are a class of liquid crystals made of aqueous solutions of plank-like molecules, which self-assemble into semiflexible chains. At a given temperature a nematic phase is formed when the system reaches a sufficiently high concentration. Among the unusual properties of chromonic liquid crystals, particularly prominent is the large anisotropy of elastic constants, which leads to new phenomenologies in confined volumes. To gain insights into the microscopic origin of this behavior, we have investigated the elastic properties of a model system that undergoes self-assembly driven nematization by using Monte Carlo simulations and an Onsager-like theory. The relative magnitude of the elastic constants and their dependence on temperature and density show the distinguishing features found in chromonic liquid crystals. We identify the relevant microscopic determinants of this behavior, and we discuss the role played by both the molecular self-assembly and the intrinsic flexibility of aggregates. © 2018 American Chemical Society.