The pricing tests for optimality in a convex programming problem are not available when the production possibility set displays economies of scale. The paper argues that indivisibilities in production are one of the major causes of such economies. The constrained optimization problems arising in the presence of indivisibilities are integer programs, and it is proposed that the unique, minimal quantity tests for such problems may shed some light on the internal organization of a large ﬁrm.
Scarf, Herbert E., "The Allocation of Resources in the Presence of Indivisibilities" (1994). Cowles Foundation Discussion Papers. 1311.