COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

Lux et veritas

COWLES FOUNDATION DISCUSSION PAPER NO. 1068

The Allocation of Resources in the Presence of Indivisibilities

Herbert E. Scarf

January 1994

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.