In Chapter 5 of the Foundations of Economic Analysis, Paul Samuelson sets forth what he calls "The Pure Theory of Consumer's Behavior," which he identifies with the analysis of utility. According to Samuelson, many economists "separate economics from sociology upon the basis of rational or irrational behavior, where these terms are defined in the penumbra of utility theory. It would seem extremely important, therefore, to know clearly what is contained in the conventional utility analysis, if only to understand the consequences of denying its validity." (at 90)
What is utility? It is not happiness in Bentham's sense, or welfare in some general sense. Nor is it a physiological or psychological. "Originally great importance was attached to the ability of goods to fill basic biological needs," writes Samuleson, "but in almost every case this view has undergone extreme modification."
Why? Because of "the recognition that a cardinal measure of utility is in any case unnecessary; that only an ordinal preference, involving 'more' or 'less' but not 'how much,' is required for the analysis of consumer's behavior."
This is a weak explanation for why consumer behavior should be considered independent of psychology or biology. Why would biology or psychology demand that preferences be cardinal rather than ordinal when a measure of consumer behavior does not? Samuelson does not say. This makes the fact that evolutionary biology, social psychology, and sociology have made a come back recently less surprising, does it not?
But how does this utility analysis of consumer behavior work then? Starting from the assumption of ordinal preferences, Samuelson postulates the existence of a utility function. To help the reader in visualizing his argument, assume for now that there are only two types of goods or activities, A and B, that a consumer can choose. If we assign the quantity of good or activity A to the x-axis and the quantity of good or activity B to the y-axis, then the utility function would be a set of lines in the x-y plane. None of these lines cross; each represents a set of x,y pairs (or bundles of A and B) which produce the same amount of utility for the consumer. The lines are called "indifference curves."
How does this get us to a theory of consumer behavior? We get there with just two additional assumptions:
The utility analysis rests on the fundamental assumption that the individual confronted with given prices and confined to a given total expenditure selects that combination of goods which is highest on his preference scale.
(at 97) In other words, given a budget, a consumer behaves so as to maximize her utility by selecting the bundle of goods that includes as many of the goods that she ranks highly as possible.
There are two assumptions here. First, that the consumer maximizes utility. Second, that the particular bundle of goods selected reveals that the consumer prefers that bundle over any other.
As one might guess from the title of this post, I see problems with one of these assumptions, and it is not the assumption of maximization. As Richard Feynman has noted, for example, the behavior of many systems (human and non-human) can be described as a constrained extremization. It would be more surprising to find out that consumer behavior does not maximize or minimize some quantity.
The problem is with the principle of revealed preference. What the principle suggests is that the preferences (and hence utility) of a consumer can be measured indirectly (i.e., revealed) by observing what bundle of goods is preferred. The problem is that, by construction, a preference is revealed only when a transaction occurs. Although everybody has experienced an increase and decrease in preferences for particular goods over time (such as hunger and thirst), the principle of revealed preferences gives us no way to measure how preferences evolve in time between transactions. Relatedly and in addition, to make a complete "measurement" of consumer preferences for an entire set of goods, one must assume that the ranking of preferences does not change over time (or at least that it changes in deterministic ways). Otherwise there is no logically coherent way to rank the entire set of preferences.
Why do economists make these assumptions? They assume revealed preferences because there are few obvious alternative methods for measuring preferences. They assume time-independence of preferences because there is no other way to measure the entire preference function. Ultimately, they make both of these assumptions because with them, one can make reasonable forward-looking forecasts about how an economy will change as a result of shifts in supply or demand for a particular good. Reasonable, but not perfect!
There are alternatives for measuring preferences. On this blog a year ago I started writing about one. Consider as an alternative to the ordinal ranking of preferences a cardinal measurement of preferences. The preferences of a consumer for a particular good could be measured by counting how often the consumer consumed the particular good within a specific window of time. This measurement of consumer preference would take units of frequency. So if a consumer ate 5 apples in a day, we would say that the consumer had preference 5 apples per day. If the consumer ate only 1 orange per week, then we would say that the consumer had preference 1/7 oranges per day.
Notice how this alternative method of measuring preferences is consistent with the principle of revealed preferences in the sense that within a particular window of time we can rank preferences for each consumer. Within the window of the one week observed, the consumer preferred apples to oranges. If the preferences of this particular consumer are stable over many weeks, then the preference function observed through revealed preferences will be either almost or exactly the same as the preference function measured directly through frequency of consumption and then ranked. This condition of stability is called "ergodicity" by physicists.
But notice also how this method of measuring preferences provides additional flexibility. In particular, the model permits for us to treat preferences as varying with the time-scale of observation. Over the course of a month, consumers might not have much interest in oranges. But over the course of a year, there may be a more substantial preference for oranges.
In addition, the alternative method of measuring preferences permits us to get more information out of the fact of exchange. Whereas before an exchange was our only source of information about the preferences of the parties to the exchange, now with our independent measurement of preferences we can use the fact of exchange as an additional source of information.
Let's say Charlie sells A to Warren for B. If we know that Charlie uses an A / week and B / day, then we can infer that Charlie probably has either some inventory of B or expects to get access to more B within the next day. The fact of exchange tells us about the model that Charlie and Warren have in mind in forecasting their future needs based on their memory of the history of their preferences. In other words, the fact of exchange in view of measured frequencies of preferences still tells us something about their subjective valuation, but it tells us something more subtle than that Charlie prefers B to A and Warren vice-versa. It tells us how often Charlie and Warren expect to use A and B given their current inventory and history of consumption.
For earlier Broken Symmetry posts on related topics see here and here.
In a nutshell, my suggestion is to replace the principle of revealed preferences with a hypothesis of periodicity. The principle of revealed preferences would still obtain in the limit of ergodicity.
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