The Cost Function

Abstract This chapter studies producers who minimize the cost of producing their output. The core notion is the cost function, which is a money-metric generalization of the input-requirement function introduced Chapter 3. This analysis follows the approach developed in Chapter 5 that combines mathematical, verbal, and geometric arguments. The discussion first characterizes the cost function’s properties in input prices: nondecreasing, concave, positively homogeneous, and Shephard’s Lemma. These properties do not reflect restrictions placed upon T. Then the discussion turns to the properties of the cost function in output. Imposing free disposability of output upon T implies that cost is a nondecreasing function of output. And imposing convexity upon T ensures that the cost function is a convex function of output.