On the Geometry of Linking Production to Cost: The Case for Cobb-Douglas

Abstract

In introductory and intermediate microeconomics courses, students are taught about production functions and cost functions but rarely are they shown a direct link between production and cost. If we assume production is Cobb-Douglas, then the CDProductionToCost.xlsx Excel file shows the link between short-run, SR, and long-run, LR, production and cost in geometric detail. This geometric approach is particularly useful in classes without a calculus prerequisite. The file has three interactive figure sheets and four information sheets. The figure sheets do not require a knowledge of Excel to operate; they can be manipulated simply using sliders and click-boxes. To focus attention on the graphical material presented, the equations that created each figure are hidden and the interactive figure sheets are write-protected. The information sheets are not write-protected so instructors can alter them as they wish. The accompanying paper provides additional graphical and algebraic detail and suggests alternative ways to use the file to deliver material to students. Although the main purpose of this file is to show the geometric link between production and cost, the supplementary sheets allow instructors (and students) to explore the underlying production function and cost- minimizing solutions that allow one to link production to cost.