While significant progress has been made toward understanding morphogen-mediated patterning in development from both the experimental and the theoretical side, the control of size and shape of tissues and organs is poorly understood. Both involve adjustment of the scale of gene expression to the size of the system, but how growth and patterning are coupled to produce scale invariance and how molecular-level information is translated into organ- and organism-level functioning is one of the most difficult problems in biology. The Hippo pathway, which controls cell proliferation and apoptosis in Drosophila and mammalian cells, contains a core kinase mechanism that affects control of the cell cycle and growth. Studies involving over- and under-expression of components in the morphogen and Hippo pathways in Drosophila reveal conditions that lead to over- or undergrowth. Herein we develop a mathematical model that incorporates the current understanding of the Hippo signal transduction network and which can explain qualitatively both the observations on whole-disc manipulations and the results arising from mutant clones. We find that a number of non-intuitive experimental results can be explained by subtle changes in the balances between inputs to the Hippo pathway. Since signal transduction and growth control pathways are highly conserved across species, much of what is learned about Drosophila applies in higher organisms, and may have direct relevance to tumor dynamics in mammalian systems.