In this study, we develop and implement an output index approach to the estimation of hospital cost functions that reflects the differentiated nature of hospital care. The approach combines the estimation of an output index within a flexible functional form. We find, in an application to California hospitals, evidence of scope economies across specialties within primary care, and diseconomies of scope within secondary and tertiary care. Minimum efficient scale is reached at larger levels of output than would be estimated by conventional techniques. These results indicate the importance of accounting for firm output heterogeneity when estimating cost functions.