Sunday, May 12, 2013

An Austrian Indifference Curve vs. The Value Scale

From the introductory undergraduate to the advanced Ph.D. courses in economics, students are taught that the concept of the indifference curve is very useful in analyzing human choice. I am emphasizing the term useful for a reason. No one ever said it was true. I don’t think anyone that understands the concept would ever try to claim that this is how humans actually make choices. However, is this the most appropriate way of conceptualizing human choice?

The answer to this question depends on what the purpose of this conceptualizing is. I will assume that we agree that the primary purpose of conceptualizing in general is the communication of ideas. Without conceptualization, ideas remain known only to the individual in whose mind they are formed.

In this article, I compare the Austrian and the mathematical neoclassical conceptualizations of consumer choice. To perform this comparison, I first translate the concept of the indifference curve into the language of Austrian economics and then compare this translated version to Rothbard's concept of the value scale. While there are similarities between the two approaches, the Austrian approach, at least in my experience, outperforms the indifference curve approach as a tool for communicating economic ideas.

The Austrian View of Choice

As demonstrated by Ludwig von Mises and later elaborated by Murray Rothbard, the basic axiom of Austrian economics states that humans act in order to move from a less preferred state into a more preferred state. They do this by using means to meet their ends. Their ends are ranked in the order of preference. Otherwise, no purposeful action is possible. Humans act to satisfy the more valued ends before the less valued ones. This is the act of choice. Something must be valued more than something else to be chosen. If two things are seen as having the same value, then there is no choice taking place. Both things can be used to satisfy the same end equally well in all respects. In the eyes of the decision maker, these two things are identical. The choice here is not between the two identical things but between any one of them and something else that satisfies some other end.

Rothbard rejected the concept of indifference as an economic concept. I don’t disagree that indifference and choice don’t make good friends. However, I will try to add some more interpretation to one of the ways mathematical neoclassical economics uses the concept of indifference--the indifference curve.

The Concept of the Indifference Curve

An indifference curve represents different bundles of two (or more) things--say, apples and oranges--where each of the bundles contains different proportions of apples and oranges but all bundles are associated with the same level of utility. (An additional assumption for the existence of an indifference curve is that the two goods are infinitesimally divisible. Thus, we need to assume that a cut up apple satisfies a certain human end in the same way as, say, a whole apple does.)

A simple example of an indifference curve would be all bundles of apples and oranges in which the total weight of the bundle equals, say, one kilogram. Here, we can have a bundle that contains only apples or only oranges or we can have any bundle in between (i.e., 1 gram of apples and 999 grams of oranges; 2 grams of apples and 998 grams of oranges, 2.1 grams of apples and 997.9 grams of oranges and so on; any combination that adds up to 1000 grams will do.)

Let us now use the Austrian framework to interpret this indifference curve. This step may be considered as heresy by some Austrians, but I'll take the risk. I see this as an exploratory exercise, and thus a valuable research tool.

An Austrian Interpretation of the Indifference Curve

If an individual, let's call him Jim, evaluated any of those bundles described above, he would attach the same utility to it as to any other bundle that he could have evaluated instead. This further means that all the bundles on the indifference curve satisfy the same end equally well. We can extend this analogy and say that the end Jim wants to satisfy is to eat one kilogram of fruit.

Note here that the relevant good, in Jim's mind, are not apples and oranges but fruit. If the relevant goods were apples and oranges, this would imply that Jim values apples and oranges as separate goods and then somehow adds the utilities he derives from the two goods into the utility of the whole bundle. This would contradict the ordinal nature of utility and therefore we can only speak of fruit as the relevant good. The apple and orange content are then attributes of the good in question. Goods are valued for their attributes, so, in this case, fruit is valued for its apple and orange content (in much the same way, say, a car is valued for its design and fuel efficiency).

If all units of fruit were free of charge, Jim would take one. Which one he would take is an absurd question from his perspective because all bundles are identical--in the sense that Jim can satisfy a given end in exactly the same way by using any one unit of fruit. Thus, an indifference curve without prices has no link with the concept of choice.

If we attach prices to the apple and orange content of fruit, each unit of fruit on the indifference curve will have a different monetary price because it contains different proportions of apples and oranges. Of course, one will buy the cheapest unit of the same thing. This is the cost minimization part of the consumer constrained optimization problem called The Dual in neoclassical consumer theory.

Suppose that the price of apples was $1 per kilogram, and the price of oranges was $1.5 per kilogram. The cheapest kilogram of fruit that Jim could buy would be the one containing only apples. In neoclassical consumer theory, we call this a corner solution because Jim chose a bundle that is at the very end of his indifference curve.

The concept of the indifference curve is an abstraction of the individual decision making process. It is a communication technique, a metaphor. As such, it is by definition unrealistic if interpreted literally.

To come back to my initial question: is the concept of the indifference curve the most appropriate means of conceptualizing the idea that humans make choices? Does this abstraction capture the essence of choice and does it communicate this essence to others better than alternative conceptualizations? Are there more succinct ways of describing choice?

The Indifference Curve vs. The Value Scale

Murray Rothbard came up with the concept of the value scale to describe choice. Using Rothbard's framework, we would say that Jim chose the $1 kilogram of fruit over the $1.5 kilogram because the cheaper kilogram was placed higher on Jim's value scale. It was placed higher because, given that Jim owns a limited amount money, this $1 kilogram of fruit allows him to satisfy more of his other ends compared to the $1.5 kilogram of fruit.

Like the indifference curves, value scales are abstract descriptions of the same observation--that Jim exchanged $1 for one kilogram of apples. So, are value scales more appropriate abstractions than indifference curves coupled with prices? In my own experience, I was far more successful communicating consumer theory to others using Rothbard's formulation. Even when I used the indifference curve approach, it became understandable to most people only after I translated it into Rothbard's language. Thus, in my experience, Rothbard's value scale approach is a more effective communication tool than the indifference curve approach.

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