Intermediate Inputs and External Economies

Is the degree of external economies (at the industry level) higher than the degree of internal increasing returns (at the firm level)? If so, what is the exact source of this difference? In this general equilibrium model in which firms producing final goods choose the degree of specialization of their technologies, external economies arise from the usage of intermediate inputs and the existence of internal increasing returns. It is frequently assumed that increasing returns are absent at the firm level while are present at the industry level. In this model, the existence of increasing returns at the firm level is necessary for the existence of external economies at the industry level. We show that the degree of external economies increases with the level of linkage effects. However, a higher linkage effect does not always lead firms to choose more specialized technologies.