On The Equivalency Of Profit Maximization And Cost Minimization: A Note On Factor Demands

Abstract

Students are often confused when introduced to the two conceptually different factor demands of the firm: those demands for inputs which originate from the firm’s desire to maximize profits, and those that are constructed to minimize the cost of producing a target level of output. These two demands for inputs are, of course, equivalent when the firm is optimizing. This note demonstrates that an often used method of teaching these concepts makes it impossible for students to visually compare these different input demands because different technologies are assumed. I provide a graphical proof of the equivalency of these factor demands by assuming the same technology in both the cost-minimization and profit-maximization problem. By employing this new analysis, it is hoped that students will gain a better understanding and instructors will gain a better teaching tool regardless of whether the course is calculus or graphically based. (JEL. A22, D21)