On the Simultaneous Existence of Full and Partial Capital Aggregates

Earlier work on aggregate production functions with capital-embodied technology showed that, when firms employ more than one capital type, conditions for partial capital (“equipment”) aggregation and for total capital aggregation differ. This paper studies simultaneously existing partial and total aggregates. Existence of a total and one partial aggregate implies existence of the complementary partial aggregate. However, simultaneous existence requires each firm's production function to be strongly separable in its capital subaggregates. The use of subaggregates like “equipment” and “plant” together with an aggregate “capital” thus implies that “plant” and “equipment” are perfect substitutes and is highly questionable.