We investigate how different models that have been proposed for solving the dark matter problem can fit the velocity dispersion observed around elliptical galaxies, on either a small scale (~ 20kpc) with stellar tracers, such as planetary nebulae, or large scale (~ 200kpc) with satellite galaxies as tracers. Predictions of Newtonian gravity, either containing pure baryonic matter, or embedded in massive cold dark matter (CDM) haloes, are compared with predictions of the modified gravity of MOND. The standard CDM model has problems on a small scale, and the Newtonian pure baryonic model has difficulties on a large scale, while a fit with MOND is possible on both scales.