Predictable Behavior: Comment

Roger W. Garrison* 

In a recent paper in this Review (1983), Ronald Heiner identifies "uncertainty in distinguishing preferred from less-preferred behavior" (p. 561) as the sine qua non of predictable behavior. Examples drawn from diverse disciplines (physical chemistry, biology, economics, and others) are evidence of the scope and richness of this insight. Yet, when the most basic law of economics, the Law of Demand, is reformulated in terms of Heiner's uncertainty-based behavior, the analysis becomes suspect. It fails to allow for the theoretical possibility of a Giffen good. The purpose of this comment is to argue that Heiner claims, at the same time, too much and too little for his new analytical framework. He claims too much by insisting on an unqualified inverse relationship between price and quantity demanded; he claims too little by failing to show how the qualifications needed in his own analytical framework parallel and complement the usual Qualifications of standard price theory. Reconciling Heiner's Law of Demand with the more conventionally conceived Law of Demand can serve to defend standard price theory and to increase our confidence in the remainder of Heiner's analysis. 

I. Allowance for the Special Case of the Giffen Good
The Giffen good, whose existence in theory is rarely denied but whose existence in reality is in serious doubt, constitutes an exception to the general Law of Demand: an increase in price is accompanied by an increase, rather than a decrease, in the quantity demanded. This paradoxical price-quantity relationship is conventionally explained in terms of the relative strengths of the substitution effect and the income effect associated with ta given price change.⁽¹⁾ If the income effect is opposite in sign and greater in magnitude in comparison to the substitution effect, price and quantity demanded will move in the same direction, and the good is a Giffen good. Acceptance of the conventional construction of demand curves, which accounts for both substitution effects and income effects, is an implicit admission of the possibility of a Giffen good--however unlikely its occurence in reality. (By contrast, Heiner claims to have formulated the Law of Demand "without any qualification for income effects..." p. 580.)
        To qualify the Law of Demand with an allowance for the special case of the Giffen good is to recognize the general limitations of the ceteris paribus assumption. If, in deriving the demand curve for a particular good, the ceteris paribus assumption is invoked in the strictest sense (which fixes income as well as all other prices, quantities, and expenditures), the resulting demand curve is a rectangular hyperbola.⁽²⁾ That is, strict fixity in all other markets, including the "market" for cash balances, would leave as a residual a fixed expenditure in the market whose demand curve is being derived. To avoid this trivial result, numerous changes throughout other markets, each of negligible magnitude, are allowed for under the assumption of ceteris paribus. This permits the derivation of a nontrivial, downward-sloping demand curve.
        The Giffen good is the result of circumstances under which the ceteris paribus assumption, even in the less-than-strict sense, cannot hold. For the income effect to be large enough to more-than-nullify the substitution effect, the good in question not only must be an inferior good but also must constitute a substantial portion of the buyers' budgets. Grain or potatoes in underdeveloped economies are the most likely kind of goods to fulfill such specifications.⁽³⁾ Under these circumstances it is logically impossible to impound all other nonnegligible price and quantity changes in the ceteris paribus assumption. Such changes can be so substantial as to constitute a substantial change in real income whose effect, in theory, may outweigh the substitution effect. Alternatively stated, the consumers of, say, potatoes are so impoverished by a rise in the price of potatoes that they must even further restrict their consumption to this inferior good. As will be seen, this alternative statement allows us to see how the limitations of the ceteris paribus assumption implicit in Heiner's framework makes equal allowance for the existence, at least in theory, of the Giffen good. 

II. Ceteris Paribus in Heiner's Framework
In the analytical framework offered by Heiner, uncertainty in distinguishing between preferred and less-preferred behavior manifests itself as a gap between the "competence" of an economic agent and the "difficulty" in selecting the most preferred behavior (See his p. 562). The competence-difficulty gap, or C-D gap as Heiner calls it, forms the backdrop for the behavior of economic agents. Gains to behavior modification are attenuated by the probability that the environmental conditions which would justify such modifications exist and are correctly perceived; losses are similarly attenuated. Under conditions of uncertainty economic agents modify their behavior only when the prospective attenuated gains outweigh the prospective attenuated losses. Heiner summarizes the implicit decision rule with an inequality that
relates the perception probabilities, which he calls the "reliability ratio," to the actual occurrence probabilities appropriately multiplied by the gain and loss functions, which he calls the "tolerance limit" (p. 556). Only when the reliability ratio exceeds the tolerance limit will economic agents actually modify their behavior.
        The application of this decision rule to an environment in which prices are changing is straightforward. A change in the price of a particular good will change the gain and loss functions associated with buying that good. Given the C-D gap, a fall in price will reverse the inequality for some economic agents causing additional agents to become buyers and existing buyers to buy additional quantities of the good. (Heiner's reasoning is slightly different from but compatible with my own: "a higher price requires purchasing behavior to be more reliable, which can be achieved only by reducing the probability of purchase" p. 580).
        It is important to recognize that in Heiner's framework the size of the C-D gap is impounded in a ceteris paribus assumption. Because it is difficult to even imagine a circumstance in which the competence of the agent and the difficulty in deciphering the environment move in the same direction and by the same "amount" (such that the C-D gap remains constant), the ceteris paribus assumption should be taken to mean that both C and D remain unchanged. In typical circumstances this assumption is fully warranted. There is no reason to believe that a change in a particular price has any discernible effect on either the complexity of the economic environment or the agent's competence to deal with it. Heiner's analysis is on as solid ground as is standard price theory.
        But paralleling the standard theory of demand, the Giffen good is associated with an atypical circumstance in which Heiner's ceteris paribus assumption cannot be maintained. When impoverished consumers are faced with an increased price in one staple that makes up a large portion of their budgets, their choice set is affected in a nonnegligible way. In the framework of standard price theory, we would say that their real incomes have been substantially reduced; in Heiner's framework, we would say that the complexity of the environment, and hence the difficulty in deciphering it, has been reduced. There is no reason to believe that the agents' "competence" has changed, but because of the new relationship between their incomes and the higher price of the staple good, their newly preferred behavior may become starkly clear; they must further limit their consumption to the staple good. Thus, the C-D gap, which must remain constant if Heiner's derivation of the Law of Demand is to yield unambiguous results, has actually been reduced in a nonnegligible way as a result of the price increase. Although this reduction of the C-D gap does not, by itself, imply that agents will necessarily buy more as a result of a price increase, it does allow us to reconcile Hiener's analysis with the theoretical possibility of a Giffen good. 

III. Conclusion
Heiner makes the claim that in the simplicity of his logic is a "clear, unambiguous implication of the Law of Demand, which we have never been able to derive with traditional optimizing methods" (p. 580). But allowing for the possibility of a Giffen good does not constitute a shortcoming of traditional methods; this theoretical possibility, rather, must be allowed for in the traditional theoretical framework and in any other theoretical framework, including Heiner's. I have shown that by focusing on the ceteris paribus assumption and its limitations, the Giffen good can be accommodated in Heiner's theory in a way that parallels the accommodation made in standard price theory. In both theoretical frameworks we can be sure that the Law of Demand holds only to the extent that the underlying ceteris paribus assumptions can be maintained. 

1. See, for example, George Stigler (1966, p. 65).

2. This problem of the ceteris paribus assumption is pointed out by Milton Friedman (1976, pp. 22-23).

3. See Stigler (1947).