We develop a profit-maximizing neoclassical model of optimal firm size and growth across different industries based on differences in industry fundamentals and firm productivity. The model predicts how conglomerate firms will allocate resources across divisions over the business cycle and how their responses to industry shocks will differ from those of single-segment firms. We test our model and find that growth of conglomerate and single-segment firms is related to fundamental industry factors and individual firm-segment productivity suggested by our simple neoclassical theory. Conglomerates grow less in a particular segment if their other segments are more productive and if their other segments experience a larger positve demand shock. We find that the growth rates of peripheral segments are very sensitive to relative productivity an that conglomerate sharply cut the growth of unproductive peripheral segments. We do find some evidence consistent with agency problems for conglomerate firms that are broken up. However, the majority of conglomerate firms exhibit growth across business segments that is consistent with optimal behavior.