Determining the price elasticity of demand: Formulas are your friend

Chapter 3: Calculus, Optimization, and You

Optimizing Is the Best Decision

You want to make the best possible decision for your business. Doing so is optimization — you’re making the optimal decision. You may be trying to maximize sales, minimize costs, and/or maximize profit. In each optimizing situation, you’re determining the best possible outcome.

Sometimes, you face constraints when optimizing. As a consumer, you try to maximize your satisfaction given the constraint of your available income. As a manager, you try to minimize the cost of producing a given quantity of output given technological constraints. In these situations, equations and calculus become very helpful tools for you.

You Want Me to Remember Calculus?

Again, you don’t have to remember calculus. Managerial economics concepts are presented without calculus. On the other hand, calculus does make things easier, and there’s nothing like an equation to dazzle the boss. Let’s be honest, if somebody wrote out a big, long equation, you and I would look at it, think “I haven’t a clue what it means,” but nevertheless be impressed. Well, the calculus you use will impress a lot of people, but more importantly, you’ll know what it means and it will help you solve managerial problems.

And as real-world situations become more complicated, calculus may be the only way to develop a solution.

Deriving derivatives

Suppose that the variable y is a function of the variable x, or

y = f(x)

Thus, a change in x’s value causes a change in y’s value. The relationship between changes in the values of x and y is described by a derivative.

You may remember from your calculus course that a derivative also represents the function’s slope at any given point.