Phase transitions of systems consisting of colloidal particles and non-adsorbing polymer in a solvent are studied theoretically in two dimensions. The colloids are modeled as hard spheres and the polymer as an ideal gas. The imbalance in osmotic pressure induced by the depletion effect gives rise to an effective attraction tail for the colloid-colloid interaction. For a monodisperse polymer, liquid-liquid separation is predicted to occur for appropriate colloid concentrations when the ratio s of the radius of gyration of the polymer to the radius of the colloidal particle is greater than 0.31, while solid-liquid separation is predicted to occur for all colloid concentrations when s is smaller than 0.31. Polydispersity of polymer is found to increase the extent of liquid-liquid coexistence, and when the average s is smaller than 0.31, and for appropriate colloid concentrations, liquid-liquid coexistence occurs provided the polymer size distribution is broad enough. Partitioning and size distribution of polymer in coexisting phases are also predicted.