Chain-chain interactions in a corona of polymers tethered to a spherical core under good solvent conditions are studied using Monte Carlo simulations. The total scattering function of the corona as well as different partial contributions are sampled. By combining the different contributions in a self-consistent approach, it is demonstrated that the corona can be regarded as a quasi-two-dimensional polymer solution, with a concentration dependence analogous to that of an ordinary polymer solution. Scattering due to the corona profile and density fluctuation correlations are separated in this approach. The osmotic compressibility is extracted from the latter, and it is shown to be a universal function of surface coverage, with some deviations at high coverage due to surface curvature effects.