MBA Math Monday Marginal Analysis by Calculus

The MBA Math Monday series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum. The first two economics exercises examined marginal analysis. whichdiscovers a firms optimal production quantity and profit. Marginal analysis problems can be posed equivalentlyin terms of tables, formulas,or charts. Thefirst exercise used data in tables. The secondexercise used formulas but without invoking calculus. This exercise uses formula and calculus. The calculus bit is the onlyaspect of this exercise that is different from the second one. The keyidea, which is explained in the full MBA Math course, is thatthe derivative of the total cost function is the marginal cost function.The derivativeexamines the incremental change in a function (e.g., y = f(x)) given a small change in the underlying value (e.g., x). Thats just what we want when we are considering the marginal cost, which shows how much total cost (e.g., TC = f(q)) has changed for a small change in quantity (e.g., q). Similarly, the derivative of the total profit function is the marginal profit function and the derivative of the total revenue function is the marginal revenue. At least its consistent. Scary as calculus may be to many incoming b-school students, the main idea is quite straightforward if you can keep your brain from locking up in fear. And the mechanics of taking the derivative of a polynomial, which is a fancy name for the functions determining cost, are refreshingly simple, taking no more than 15 minutes to recover from the memory vault of lost ideas from high school. Exercise: Suppose a competitive firm has as its total cost function: TC = 24 + 2q2 Suppose the firms output can be sold at $66 per unit. Using calculus and formulas (but no tables) to find a solution, how many units should the firm produce to maximize profit? Solution (with audio commentary): click here Prof. Peter Regan created the self-paced, online MBA Math quantitative skills course and teaches live MBA courses at Dartmouth (Tuck), Duke (Fuqua), and Cornell (Johnson).