## 4.11Appendix Introduction

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Chapter 4 Appendix

Chapter 4 Appendix: The Calculus of Utility Maximization and Expenditure Minimization

In the chapters you’ve read so far, you’ve probably noticed that we use several different approaches when explaining microeconomic theories and applications. One method is mainly intuitive: Tell a story to illustrate an economic concept or discuss the logic of a model and its implications. This method of economic analysis goes back to Adam Smith and the invisible hand. A second method is the graphical approach. You only have to say “supply and demand” to conjure up a simple but powerful representation of a market. Finally, you’ve seen some simple mathematical models such as the algebraic representations of supply and demand curves in Chapter 2 and the consumer’s budget constraint in Chapter 4. Each of these approaches provides a different window into understanding economic concepts.

Those of you who are familiar with calculus have yet another way to approach microeconomics. The tools of calculus are a natural fit with economics, and most economic models are formally derived using calculus. For some people (especially economists), it’s easy to become so caught up in the math that the real economic ideas get lost. We don’t want you to fall into that trap. That’s why we present the calculus as a supplement to the intuition that we develop in the chapter. The calculus appendices provide an additional set of tools to examine the economic decisions and interactions discussed in the chapter. The logic of the models and the intuition from the chapter are still here in the calculus, only in another form.

So, don’t think of the calculus that we explore in the appendices as a substitute for the logic, graphs, and algebra we use to explain microeconomics in the chapters. Instead, think of these techniques and the calculus as complements. As you learn more about microeconomics, you will find that each of these different approaches to understanding microeconomics may be more or less useful depending on the circumstances.