The questions of how healthy colonic crypts homeostatically maintain their size, and how homeostasis is disrupted by driver mutations, are central to understanding the early stages of colorectal tumorigenesis. We propose a non-spatial, three-type branching process to model the dynamics of the hierarchy of different cell populations residing in colonic crypts. Our model is simple in its formulation, allowing us to easily estimate the model parameters from experimental studies. We are able to solve our model analytically, without resorting to computationally intensive simulations. Model results agree well with data from human colonic crypts, being able to capture the considerable variance in crypt size observed experimentally. Furthermore, by taking into consideration the effects of APC and KRAS mutations on the number and proliferation characteristics of epithelial cells, our model is able to explain the increase in crypt size observed in early stages of colorectal tumorigenesis.