Consider Sammy, whose appetite is exclusively for clams and potatoes (there’s no accounting for tastes). He has a weekly income of $20 and since, given his appetite, more of either good is better than less, he spends all of it on clams and potatoes. We will assume that clams cost $4 per pound and potatoes cost $2 per pound. What are his possible choices?

Whatever Sammy chooses, we know that the cost of his consumption bundle cannot exceed his income, the amount of money he has to spend. That is,

Consumers always have limited income, which constrains how much they can consume. So the requirement illustrated by Equation 10-1—that a consumer must choose a consumption bundle that costs no more than his or her income—is known as the consumer’s budget constraint. It’s a simple way of saying that a consumer can’t spend more than the total amount of income available to him or her. In other words, consumption bundles are affordable when they obey the budget constraint. We call the set of all of Sammy’s affordable consumption bundles his consumption possibilities. In general, whether or not a particular consumption bundle is included in a consumer’s consumption possibilities depends on the consumer’s income and the prices of goods and services.

Figure 10-2 shows Sammy’s consumption possibilities. The quantity of clams in his consumption bundle is measured on the horizontal axis and the quantity of potatoes on the vertical axis. The downward-sloping line connecting points A through F shows which consumption bundles are affordable and which are not. Every bundle on or inside this line (the shaded area) is affordable; every bundle outside this line is unaffordable.

As an example of one of the points, let’s look at point C, representing 2 pounds of clams and 6 pounds of potatoes, and check whether it satisfies Sammy’s budget constraint. The cost of bundle C is 6 pounds of potatoes × $2 per pound + 2 pounds of clams × $4 per pound = $12 + $8 = $20. So bundle C does indeed satisfy Sammy’s budget constraint: it costs no more than his weekly income of $20. In fact, bundle C costs exactly as much as Sammy’s income. By doing the arithmetic, you can check that all the other points lying on the downward-sloping line are also bundles at which Sammy spends all of his income.

The downward-sloping line has a special name, the budget line. It shows all the consumption bundles available to Sammy when he spends all of his income. It’s downward sloping because when Sammy is consuming all of his income, say consuming at point A on the budget line, then in order to consume more clams he must consume fewer potatoes—that is, he must move to a point like B. In other words, when Sammy chooses a consumption bundle that is on his budget line, the opportunity cost of consuming more clams is consuming fewer potatoes, and vice versa. As Figure 10-2 indicates, any consumption bundle that lies above the budget line is unaffordable.

Do we need to consider the other bundles in Sammy’s consumption possibilities, the ones that lie within the shaded region in Figure 10-2 bounded by the budget line? The answer is, for all practical situations, no: as long as Sammy continues to get positive marginal utility from consuming either good (in other words, Sammy doesn’t get satiated)—and he doesn’t get any utility from saving income rather than spending it, then he will always choose to consume a bundle that lies on his budget line and not within the shaded area.

Given his $20 per week budget, which point on his budget line will Sammy choose?