Stigler Chapter 4: The Theory of Utility Part 1

In similar fashion to Mas-Colell, Stigler is creating a dual theory. One side is producer theory, which describes behavior under the goal of profit maximization. The other side is consumer theory, which describes behavior under the goal of utility maximization.

Utils

Profit maximization has a clear meaning, at least from an accountant. Utility maximization is more complex. What the heck is a util? "The answer- that a util is a unit of utility- itself has zero utility" (Page 43) Why would someone maximize it? Utils, and utility theory, is an attempted to reduce enjoyment/pleasure/happiness/utility down to one value. More utils means the person is happier.

Utility theory came into economics in the 19th century through psychological explanations. Starting with their godfather, Jeremy Bentham, these theorists saw human behavior as a product of increasing pleasure and decreasing pain. The net of this would be a person's utils. This psychological theory reaches its pinnacle with the work of Francis Edgeworth's Mathematical Psychics. (While this might be the best book title ever, most economists only remember Edgeworth for his famous box.)

This theory fell apart over time. Stigler claims economics has abandoned this simple calculus and

The simple measure of utility, the comparisons of utilities derived by different people, the use of interpersonal utility comparisons to support public policy proposals- all were gradually abandoned in part or in whole. What was retained was the concept of what we may term a rational consumer. Pg 43

Now economists do not care about measuring utils, since the value of a util is meaningless. Instead, utility functions allow for ranked preferences to become a single number. While Stigler admits it is impossible, he assumes that all goods and bundles of goods are compared and ranked for consumption.

A compete ranking is impossible for several reasons. First, we can never truly separate out exchange and consumption value. Stigler is trying to isolate the latter. Secondly, it involves an enormous number of combinations. Do you prefer 2 tables, a chair, and a ham sandwich above 4 apples, 10 elephants, 3 sandwiches, and a glass door? Also, Stigler claims that sometimes people are indifferent. Although Rothbard would disagree, indifference is a popular concept in economics. How do we rank two goods that the consumer is indifferent between?

Nevertheless, Stigler still constructs a utility function and the always popular indifference curves to represent preferences. The number of utils does not matter, only the ranking. If two options bring the same utility, the consumer is indifferent and these two option fall on the same indifference curve. It is simply a graph that showing a utility function. It is much easier to digest than a ranking system comparing every possible combination of goods.

At this point Stigler has made no further assumptions about what is rational. Any set of preferences can be represented by indifference curves, although they could be quite strange.

Limits on Preferences

This openness causes some problems, because the standard is too weak for meaningful and workable analysis. How can economists make predictions, if literally any beliefs are possible? Stigler adds a few assumptions to make life easier.

First, he assumes that all goods are good. We want more of every good. Even bads, such as pollution or Nickelback music, become goods through redefining the term as "absence of Nickelback." This leads to downward sloping indifference curves. If I have more of one good, I must have less of the other to be indifferent. Having only goods also ensures that a higher indifference curves are better. Saying that the consumer always to maximize utility mean that he wants the highest possible indifference curve, away from the origin.

Second, he assumes that goods are continuously divisible. While Austrian often work in discrete rankings, Stigler, just like Mas-Colell, acts like every good can be divided again and again. This assumption allows for indifference curves to actually be curves, instead of discrete points.

This also ensures that indifference can exist. Assume I prefer 9 apples and 14 bananas (9,14) to 1o apples and 10 bananas (10,10), which is prefered to 9 apples and 11 bananas (9,11). If I can infinitely split my bananas, there exists some amount of bananas with 9 apples (9, X) that is indifferent to (10,10). Indifference is not just assumed, but result from assuming divisibility.

Convexity and the Budget Line

Stigler also assumes that indifference curves are convex to the origin. As a historian of economic thought, Stigler explains how the assumption developed.

Originally, economists used introspection to prove convexity. The utility theorists mentioned earlier assumed that consuming goods produced utility. However, each extra good provided less and less utility, the famous diminishing marginal utility.

If each extra good X provides less and less utility, less and less of good Y is required to stay on the same indifference curve. This changing rate of substitution is represented by the slope of the indifference curve, which decreases away from zero consumption of a good.

While this is a true analysis and often used to explain convexity, Stigler sees one problem with it. This introspective analysis implicitly assumes a world with one good and that the marginal utility only depends on the amount of the good. However, goods can affect the marginal utility of each other. If I have more bread, each unit of butter is better. If I have no bread, butter does not much appeal. This connection across goods breaks the clear link between decreasing marginal utility and convex preferences.

Instead of simply assuming convexity like Mas-Colell, Stigler insists that it is an empirical observation. Empirically, economists know indifference curves are convex. To understand why, we need to analyze the constraint on consumers, their budget.

The Dreaded Budget

The fact that consumers cannot have all the bread, butter, and absence of Nickelback that they want is simple. They cannot afford it. While most of this chapter has not included money, it is easier to think  in terms of money. Each consumer has a certain amount of money and can only buy that much.

This translates into a budget line when put on a graph. For a consumer choosing between two goods, it is a line that marks off what a consumer can buy, like the straight lines in the picture below. Without the constraint of a budget, improving utility is easy: consume more of any good. With a budget, the consumer needs to make trade-offs.

Should he spend money on this or that? Bring it full-circle, he will choose the bundle that maximizes utility. Combining the budget with indifference curves shows that the highest indifference curve (the most utility) is where the budget touches the curve at one place.

This touch can happen in two ways. First, the consumer could choose to spend all of his income on one good shown by U1 below. The last small bit of money is better than spending a penny on a car (the car breaks the divisibility assumption).

Another possible indifference curve could be tangent to the budget, such as U2 above. This happens when the rate of substitution between money and cars, shown by the slope of the prices, is the same as the ratio of prices.

Stigler claims that U2 is more common. People consume multiple goods and this happens when the indifference curves are convex like U2.

Mr. (or Ms.) Rational Consumer

But I thought we were trying to analyze rational consumers. None of this is about rationality. We are putting stuff on graphs.

What makes an actor rational? Some definitions range from the weak or almost meaningless1 to obviously exaggerated2. Stigler's rational consumer is somewhere between.

For Stigler, a rational consumer satisfies three criteria-

  1. His tastes are consistent.
  2. His cost calculations are correct.
  3. He makes those decisions to maximize utility.

Consistent tastes is a minimal requirement. It is like transitivity in Mas-Colell. If he prefers A to B and B to C, he must prefer A to C. It does not say whether these preferences are "logically harmonious." People can gamble and buy insurance at the same time.

Correct Calculations is a stronger requirement on preferences. Stigler elaborates with a few examples.

One example is about a Christmas fund. People have two options for Christmas savings. The first is the bank where the savings will earn interest (the book is really dating itself with this example). The other is a Christmas fund that will not earn interest and the money cannot be withdrawn.

However, people do use Christmas funds. This requires the introduction of another good, protection against future lack of willpower. Stigler is quick to point out that if the analysis ends here, any action is justifiable. In order to keep up the predictive power, we must consider the exchange as involving two goods, one is the interest and the other is protection against lack of will power. We still can predict then. If interest rates rise, it will become relatively more costly for people protect against themselves. We should see a drop in Christmas funds when interest rates rise, which Stigler claims is true.

Another example is more important, interesting, and controversial. Rational people will pay the same amount for the same bundle of goods. People are indifferent between a $2 beer with a $5 burger compared to a free beer and a $7 burger. They can calculate. However, as anyone who looks at "buy one get one free" can tell, this is not always true. People do not always calculate correctly.

However, if we assume people cannot calculate this, what do we predict? Given two identical options, the consumer acts differently. Until a better theory of when exactly these errors in thinking occur develops, such as behavioral economics, economists stick to the assumption that costs are correctly calculated.

Maximizing utility is the last characteristic of a rational consumer. It is the heart of the argument. This chapter starts off by saying that utility maximization is the mirror of profit maximization. However, this is the most controversial assumption, at least with non-economists.

Clearly, the skeptic does not try to minimize utility, because he is alive. How can we prove that people maximize utility? Stigler points to introspection. Our actions try to achieve our goals. It is a Rothbardian type of argument.

What would it mean to not maximize utility? It would mean that a person could be happier, but choses not to be. To the believer in rationality, this wins the argument. To the skeptic, this is not enough evidence. Stigler assures the reader that there is more evidence. For now, he is happy with introspection.

Analysis

This chapter is the most interesting chapter in my journey yet. It may seem like the same old theory, but from a methodological point of view. Stigler highlights the difference between the different authors. Sometimes he is right. Sometimes he is wrong.

As someone who has read a fair amount of Mises and Rothbard, I cannot help but smile when economists talk about "utils." Still, I am glad to see Stigler defend his use. Mas-Colell has a qualifier that the number of utils is meaningless, but leaves it at this. Stigler goes deeper.

I doubt some of Stigler's claims though. Has economics really abandoned the utilitarian calculus? Do economists really not try to make interpersonal comparisons of utility? Mas-Colell cannot even finish three chapters without interpersonal comparisons. My own microeconomics courses went through basic consumer and producer theory and then *bam* comparing utilities.

Of course, Stigler in 1982 cannot be held accountable for modern economics. Yet, in the next part of this chapter, Stigler goes on to develop an idea of consumer surplus, which seems awfully close to trying to measure utility through money. Economists sometimes forget the earlier limitations they placed on their theory. James Buchanan has a great quote here.

His three assumptions about tell a lot about Stigler's method. Instead of just making assumptions to limit the subspace of an equation so it is solvable, Stigler attempts to prove each one differently. He does not have a universal criteria, but it is more ad hoc. His first assumption is for clarity. Redefine the variables so that everything is good. His second assumption is for simplicity. It is easy to work with continuous goods and functions than with discrete functions. His third assumption comes from empirical evidence. Consumers seem to have convex preferences, so we should just assume that. These assumptions do not need an explicit definition, such as those in Mas-Colell. Instead, they are reasonable assumptions that people can understand.

Luckily, Stigler is always clear about why he is taking these short cuts. It is to increase the applicability and predictability of a theory. Of course, restricting a theory means that Stigler's economics is not very good at explaining some aspects. As always, there is a trade of between breadth and predictability. Stigler comes down on predictability. Of course, some Austrians will say that economists like Stigler are deceiving themselves into thinking they have predictive power.

There are many more gems for methodology students. I urge others to pour over it.


1. Consumer did X, because he wanted to. He acted on his beliefs. He is rational. This is closely related to the revealed preference argument introduced in Mas-Colell. It is more of definition than an explanation.

2. This type includes caricature economic-man who maximizes simply maximizes his income with perfect foresight. Often associated with rational-expectations, this is more a straw-man than economics promoted by Sargent or Lucas.

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