DERIVING A CUBIC TOTAL COST FUNCTION FROM A CUBIC TOTAL COST CURVE

The standard treatment of short run cost curves in managerial economics and intermediate microeconomics classes starts with a cubic total cost function, TC(Q) = a bQ cQ2 dQ3 and derives the various per-unit cost functions. These functions are then displayed on two graphs – one depicts TC (as well as its components, variable and fixed cost) in (Q, $) space. The other depicts marginal cost, MC, average variable cost, AVC, and average total cost, ATC in (Q, $/Q) space. This article presents a series of linked problems that move the student in the opposite direction. Students are asked: Given the graph of a cubic TC curve, can one geometrically derive estimates of coefficients a, b, c, and d on which this curve is based? The answer is yes. In the process, students learn in a more intensive fashion than simply remembering the functions themselves, the difference between per-unit cost and total cost. The ultimate goal is to provide students with a more grounded understanding of the relationships that exist between the various short run cost curves and why the curves hang together as they do. Two final questions link this cost information to competitive market analysis.