Awkward Utopia

This summer I have been reading a little bit of Becker’s 1971 textbook, Economic Theory. I love this book because it is relatively short and has much interesting commentary which is omitted from other micro theory textbooks. The book’s strength is also its weakness—math often appears as an after thought.

Last night I read a section that confused me and thus reinforced why math is useful in economics. Prior to this section, Becker argued that the law of demand is not a consequence of rational behavior, but rather a consequence of scarce resources (I’ll discuss this idea in a later post). When he later proceeds to develop the theory of utility maximization, he stops to consider the motivation for doing so. Why consider this theory if we don’t need it to get the most important result of economics, the law of demand?

Becker argues that the theory implies “that consumers prefer more goods to less.” This implication is extremely important, as Becker explains, and is worth our continued investigation:

This is an extremely powerful implication that can explain why consumers end up on the boundary of their opportunity sets, why they buy at the lowest price known to them, or even Adam Smith’s famous observation about the propensity of people “to truck, barter, and exchange one thing for another.” It also provides an incentive to invest in education, on-the-job training, information about the quality and prices of goods, and other human capital.

So where’s the confusion? In the more mathematical theory that I am familiar with, we begin by assuming that consumers prefer more goods to less. This statement is not an implication of the theory, but an assumption. This assumption is called monotonicity. [A less specific assumption that is often used is called nonsatiation: consumers don’t necessarily want more of a good, but there always exists some bundle of goods, not necessarily affordable, such that the consumer is better off at that bundle than at their current bundle.]

Thus there is a fork in the road: who is correct: Becker or the other micro textbooks? One possible compromise is possibly a redefinition of commodities. That is, suppose we have one consumer who prefers to consume nothing and die. Then this consumer clearly does not prefer more goods to less. We could redefine the relevant commodities to this consumer, however. Since the consumer does not prefer more goods to less, these “goods” are “bads”. So if we define a new commodity Y as “lack of X” then the consumer prefers more of Y.

This redefinition is ad hoc, however, and certainly this should not be seen as a powerful implication of the theory, as Becker claims. It should be seen only as a useful convention. [Also note that such a convention is typically discussed when justifying the assumption of monotonicity.]

On page 27 Becker provides a proof of his claim. Here we see that his earlier claim is actually not true and he was really speaking of a more specific statement: Of all goods which a consumer chooses to consume in positive quantities, the consumer prefers more to less of those goods. Becker provides a proof by contradiction:

If less of any good were preferred to more, and if the good had a non-negative price, a consumer would increase his utility by reducing his demand for that good until he either consumed none of it or preferred more to less.

If a consumer were “satiated”—indifferent between more and less of all goods—and if work were “irksome,” he would reduce his hours worked and thus his income until either his income (or at least his earnings) vanished or he preferred more of some goods to less; he would then consume only these goods in positive quantities.

It is in this sense that utility theory implies that more is preferred to less of all goods actually consumed.

This more specific statement is indeed a consequence of utility maximization. It is essentially an interpretation of the first order conditions for the problem: if at the optimal point, the consumer chooses a positive amount of a good, then marginal utility at that point must be positive, which implies that an increase in the amount of the good consumed increases utility. That is, more is preferred to less, for that good, at that particular level of consumption.

Let’s consider the reasons why Becker believes this implication to be important. First, why do consumers end up on the boundary of their opportunity sets? In the most basic theory we omit the labor/leisure choice and instead assume consumers just have some money to spend. In this case, we need to assume nonsatiation if we want to guarantee that the optimal bundle is on the boundary of the opportunity set.

In the extended model, where a consumer’s resources depend on their labor/leisure choice, then Becker’s analysis is quite clear: A consumer would never consume on an interior point, assuming that labor is undesirable. If an interior point was preferred, the consumer would increase consumption of leisure, which would continue until the budget line touches the original interior point.

Next, why do consumers buy at the lowest price known to them? If they are purchasing a good, then they prefer more to less of it. If they could obtain the good at a lower price, then they could purchase more of the goods, and hence would do so. Behavior otherwise is inconsistent with maximization.

I’m not sure exactly what Becker means when he refers to Adam Smith’s quote. My only guess is that he means that if consumers didn’t prefer more to less of some goods, then they wouldn’t truck, barter, and exchange.

Finally, since consumers prefer more of some goods to less, this preference provides an incentive to increase their resources. Consequently they may invest in human capital. They may also search for quality and price information—which may allow them to consume more.

So who was right, Becker or the standard micro texts? In the end, they’re both right. Becker’s initial discussion was somewhat imprecise, and it was this lack of precision which led to an apparent disagreement. When he spoke more specifically later on, it became clear that no such disagreement existed.

Mathematics often makes it easier to make more precise statements, and this is why I continue to support its use in economics. On the other hand, I also bemoan the relative lack of Becker-esque analysis in economics. Despite being fairly familiar with the main micro theory arguments, I hadn’t thought of the labor/leisure argument for why one always consumes at the boundary of the opportunity set before, and this seems fairly important. It was Becker’s discussion that led to such thoughts, not the dry math common in modern micro textbooks.