As we’ve just seen, we can find Sammy’s optimal consumption choice by finding the total utility he receives from each consumption bundle on his budget line and then choosing the bundle at which total utility is maximized. But we can use marginal analysis instead, turning Sammy’s problem of finding his optimal consumption choice into a “how much” problem.

How do we do this? By thinking about choosing an optimal consumption bundle as a problem of how much to spend on each good. That is, to find the optimal consumption bundle with marginal analysis, we ask whether Sammy can make himself better off by spending a little bit more of his income on clams and less on potatoes, or by doing the opposite—spending a little bit more on potatoes and less on clams. In other words, the marginal decision is a question of how to spend the marginal dollar—how to allocate an additional dollar between clams and potatoes in a way that maximizes utility.

Our first step in applying marginal analysis is to ask if Sammy is made better off by spending an additional dollar on either good; and if so, by how much is he better off. To answer this question we must calculate the marginal utility per dollar spent on either clams or potatoes—how much additional utility Sammy gets from spending an additional dollar on either good.