As stated in this chapter, three specific forms of this function are used in economic analysis: the cubic, the quadratic, and the linear. Microeconomics theory relies primarily on the cubic equation because it encompass the possibility of increasing returns to a factor as well as diminishing returns. The quadratic form of the cost function implies that only the law of the diminishing returns affects the short-run relationship between a firm output and its variable input. The linear form indicates that neither increasing nor diminishing returns to a factor take place in the short run as the firm uses additional units of its variable input. In this appendix, we use calculus to state the cubic equation, the one most frequently used in economic theory.