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158 Principles of economics Methodology and the individual decision-maker 159
and hence that the decision-maker™s theory of knowledge and methodology Market demand depends on the consumers™ methods of learning
can be taken for granted.
Several alternative methodologies might be employed in the process of
interacting in the market. In addition to the methodological doctrines
THE METHODOLOGY OF DECISION-MAKERS identified in Chapter 6, namely Apriorism, Inductivism and Scepticism, I
will now include the Conventionalist methodology mentioned above and
Economic theorists must recognize many different views of knowledge and
the well-known methodology of Milton Friedman which I have elsewhere
methodology since the decisions based on them will usually lead to
called Instrumentalism.5 Using these alternative methodologies, let us now
different patterns of behaviour. I will try to demonstrate this proposition in
consider various types of consumers facing the same static market
the narrow context of the typical neoclassical theory of decision-making.
situations (in which all exogenous variables are fixed). Assume that all
consumers have identical incomes and identical true utility functions.
Demand depends on the demander™s theories However, let us also assume consumers neither know these functions a
priori nor do they share the same opinions about their utility functions.
Consider textbook ordinal demand theory. According to the textbooks, the
demand curve for any individual is merely the locus of all price“quantity An inductivist consumer. If one has to learn whether one is actually
combinations at which the individual™s utility is maximized for the given maximizing utility by comparing actual bundles consumed, how does
income and prices as well as the given utility function. How does the one decide the issue? Some believe that you should not jump to conclu-
individual know all the givens? Prices and income may be sufficiently sions and thus that you never know the correct utility function until you
objective that it does no harm to argue that the individual knows them, at provide an inductive proof “ all done without ever making any assump-
least momentarily, when making planned purchases. On the other hand, tions. Such a consumer will always be forced to keep trying new
assuming that the individual knows his or her private utility function begs bundles. Although facing a static situation, an inductivist consumer
far too much. A particular bundle of quantities of goods actually can be would appear never to be satisfied.
said to be better than any other (in order to explain the choice of that A sophisticated inductivist consumer. Few would think today that
bundle) only if the individual is presumed to compare that bundle with all anyone just collects the facts without thinking ahead. But, even if one
other conceivable bundles. Of course, given a typical utility function and a arbitrarily adopts a theory of the nature of one™s utility function, one can
little calculus such a choice can be justified. But knowledge of the utility still never be satisfied until that theory is proven true. This approach can
function is equivalent to comparing all pairs of bundles. Like any other also lead to the appearance of unstable buying patterns. Nevertheless, if
universal statement, this one cannot be shown to be true in real time since the theory is true, over time we should expect to see the buying pattern
such a demonstration would require an infinity of evidence (and time). But, converging to a stable point.
of course, such an inductive proof is actually unnecessary.
An Apriorist consumer. Since Apriorists begin ˜knowing™ the true utility
In ordinal demand theory all that the individual needs is an assumption
function (either by assumption or introspection), no market evidence
about the nature of his or her utility function. Like any other assumption,
could ever cause them to change their mind. The pattern is not only
we assume that it is true only because we do not know whether it is
stable but invariant.
actually true. In the case of the consumer, the plans for purchases must be
A conventionalist consumer. Given the many conceivable utility func-
made on the assumption of a particular utility function. The assumed utility
tions, how does one pick one to start with? If one gives up the require-
function can be true or false. How does the individual actually know that he
ment of a complete proof, various criteria can be adopted to appraise
or she is maximizing utility with his or her latest purchase? That is, how
one™s theory of one™s utility function. In effect, the consumer need only
does the individual learn what the true nature of his or her utility function is
be a good econometrician. No claim is made that the true utility function
except by making purchases? It is precisely the ˜learning by doing™
is found, but only the best available according to the evidence and the
situation that Lachmann mentions [1982]. The individual™s pattern of
adopted criteria. The pattern of consumption behaviour will depend on
purchases must over time reflect his or her approach to learning the true
the method used to process data. For example, how many tests of current
utility function. Thus, methodology must play an integral part in our
theory are required before concluding one knows or does not know the
explanation of demand.
© LAWRENCE A. BOLAND
160 Principles of economics Methodology and the individual decision-maker 161
true utility function? Competent conventionalist consumers might test inductive learning for granted. The same thing could be said for the
their theory every third trip to the market and still be able to explain traditional neoclassical theory of the consumer. While convexity of
away numerous refuting observations before being forced to change preferences is usually explicitly asserted or assumed, no discussion is
their pattern of behaviour. provided to indicate how the individual learns which bundle will actually
maximize his or her utility. If the individual™s preferences are actually
A scepticist consumer. At the other extreme there are consumers who
convex, then I would suggest that the individual™s learning process is taken
are always sceptical about proving any theory true. These consumers
for granted because neoclassical theorists also take inductive learning for
will change their mind about their personal utility functions the first
granted. If they do not, then there is no reason to believe that the individual
time some purchased bundle does not meet their expectations. While the
will ever be maximizing his or her utility. If my claims are correct then we
conventionalist consumers can tolerate occasional disappointments and
can safely predict that much methodological work still must be done even
thus seldom alter their consumption patterns, the scepticist consumers
within the otherwise successful neoclassical theory of decision-making.
will be jumping all over the map.
An instrumentalist consumer. It is not always clear what instrumentalist
consumers might do since the truth of their theories of their utility func- NOTES
tions supposedly does not matter. They might act as if they liked their 1 The view that people learn inductively is a variant of the doctrine of
purchases when indeed they detested them. As long as their social role Inductivism which I discussed in Chapter 1, note 5. According to this view
does not change, one could predict that the instrumentalist consumers whenever one collects any fact needed to obtain the required inductive proof,
one is learning. Over three centuries ago this view of knowledge and learning
might continue to buy the bundle of goods that is most useful for their
was considered the essence of enlightenment since it countered those who
chosen careers. Any change in career will be accompanied by a change
required religious authority for knowledge claims. Unfortunately, the logical
in the consumption pattern [see again pp. 150“2]. foundation for the enlightened view was undermined by the late-eighteenth-
century arguments of David Hume and others who noted that such a view of
These crude examples should be sufficient to demonstrate the potential
learning leads to an infinite regress. If all knowledge must be based only on the
role for methodology in the explanation of decisions within the domain of facts, then it calls into question how we learned that knowledge must be
neoclassical theory. When it is recognized that one™s utility function is not inductively proven. Whatever our answer, it begs a question of methodology
known a priori and must be learned, it must also be understood that an which must also be inductively proven but this leads to a further question
requiring an inductive meta-methodology, and so on. But worse, given this
appreciation of methodology is necessary to explain the pattern of
infinite regress, even when the knowledge is true, there may be no way to prove
behaviour in the competitive process of Hayek and Lachmann. In the
it true. Failure to prove its truth, inductively or otherwise, does not prove the
typical neoclassical model two individuals with identical utility functions, knowledge is false [see further Boland 1982a, Chapter 11].
identical incomes, and facing the same prices, would choose the same 2 Israel Kirzner invited me to contribute to a book of essays honouring Professor
bundles of goods. The examples above show that this conclusion fails to Lachmann [Kirzner 1986]. The remainder of this chapter is based on my contri-
bution, parts of which are reprinted here by permission of New York University
hold if they try to learn their (identical) utility functions using different
Press.
learning methodologies.
3 See again the discussion of Inductivism in note 5 of Chapter 1.
4 I discussed this view of knowledge in note 20 of Chapter 2.
5 Instrumentalism, as it is practiced in neoclassical economics, views theories as
The methodology of stable markets and convex preferences
useful instruments either for understanding the economy or for assisting policy-
makers. The key element of Instrumentalism is the view that theories should not
If it is now recognized that Hayek™s view of the competitive process gets to
be judged on whether they are true or false but on whether they are useful for
the heart of the neoclassical market then it should also be easy to see that
the purposes at hand. Policy-makers are only required to act as if their theories
his view runs parallel with my alternative view of the decision-maker. are true. See further Boland [1979a; 1982a, Chapter 9].
Hayek™s view, unlike neoclassical economics, does not depend on the
actual achievement of an equilibrium. It depends on the progressive
learning that must take place by virtue of the presumed stability of the
market in question. Hayek did not actually try to explain how individuals
learn what is necessary to make a market decision. Instead, he took
© LAWRENCE A. BOLAND

Part IV

Some technical questions
© LAWRENCE A. BOLAND

12 Lexicographic orderings




[Economics] should have that delicacy and sensitiveness of touch
which are required for enabling it to adapt itself closely to the real
phenomena of the world ...
Alfred Marshall [1920/49, p. 635]


The questions of the pervasiveness of equilibrium and maximization are
fundamental and thus little of neoclassical literature seems willing or able
to critically examine these fundamental ideas. This does not mean that
neoclassical writers do not venture criticisms. There are many critiques but
they are almost always about technical modelling questions such as what
way to formally represent the consumer™s utility function. As I noted in
Chapter 1, the question of whether to assume a consumer is a maximizer is
never put into question, only the assumptions about the nature of the
function. I now turn to an examination of some of the technical disputes
surrounding neoclassical theory to see if they are worth while criticizing. In
the next three chapters I will examine key ideas employed in neoclassical
demand theory that have acquired a status that puts them beyond criticism
even though that status is unwarranted.
While it may be reasonable to put maximization beyond question along
the lines discussed in Chapter 1, it is not obvious that the form of the utility
function should be limited a priori. Nor is it obvious why the infamous
Giffen good (i.e. the case of an upward sloping demand curve) should be
acceptable in any demand theory which is used in conjunction with supply
curves to explain price determination in the market. While a ˜generalized™
demand theory might be more convenient for mathematical model-builders,
those neoclassical economists who wish to use their theory to deal with
practical problems will not find such models very helpful. For example,
economists who try to evaluate public policies by calculating net gains or
losses in terms of ˜consumer surplus™ (which is represented by the area
under the demand curve but above the horizontal line representing the
© LAWRENCE A. BOLAND
166 Principles of economics Lexicographic orderings 167
price) will be stymied by an upward sloping demand curve. Similarly, a clear understanding of the concept of an L-ordering.
economists who see merit in a government™s ordering its priorities before One way to understand the concept of an L-ordering is to consider it to
ordering alternative projects of a similar priority will find it difficult to be a solution to the methodological problem created by the recognition of a
form a sensible social utility function over all conceivable projects. That is, multiplicity of relevant criteria for comparing goods. To the extent to
some economists consider lexicographic orderings to be a reasonable which L-orderings solve a problem they must necessarily be ad hoc in the
approach to public policy decision-making [see Encarnacion 1964] but, sense that they are invented to do the intended job. If we attempt to
unfortunately, most neoclassical demand theorists are taught to believe that eliminate the ˜ad hocery™, we merely create the same (methodological)
the concept of a lexicographic ordering is not plausible. The purpose of this problem at a ˜higher level™, which means that the use of L-orderings as a
chapter is to examine the issue in demand theory concerning the difficulty means of explaining any consumer™s choice can lead to an infinite regress.
of using lexicographic orderings (L-orderings) in lieu of ordinary But this is not a sufficient reason for rejecting L-orderings since to the
monotonic utility functions. In the next two chapters I will examine the extent that they represent the reasons why an individual chose one
issue of whether demand theory can or should preclude the possibility of particular bundle over any other affordable bundle, every form of ordering
upward sloping demand curves. is ad hoc and if questioned would lead to an infinite regress.


L-ORDERINGS THE DISCONTINUITY PROBLEM
A formal preference ordering represents how a given consumer would If there are good reasons for rejecting the use of the L-ordering in demand
rank-order two or more bundles of goods (where a ˜bundle™ specifies a theory, perhaps we will find them by examining how L-orderings might be
quantity for each good being considered). A monotonic utility function can used. There is one classic problem where it is clear that there are formal
form the basis for such a preference ordering in a direct way. Obviously, problems with the notion of an L-ordering. This classic problem (not to be
when comparing any two bundles, the preferred bundle yields the most confused with the methodological problems below) arises directly when-
utility according to the utility function. The process whereby the individual ever it is assumed that the consumer is using goods themselves as an index
goes about determining the utility for any bundles is seldom considered. in his or her L-ordering. Namely, if a person always prefers a commodity
The lexicographic ordering seems to appeal to those who think the process
Y
of ranking or assigning utility should be apparent.
Z′
The paradigm of an L-ordering is the dictionary and its ordering of
words. It says that the order in which words are listed in the dictionary is
alphabetical. And those words with the same first letter are sub-ordered
Worse than
according to their second letter, and so on. The L-ordering in the case of
A set
bundles of goods might say that the preferred bundles are those which give
Better than
the most nutrition. And of those bundles which give the same nutrition,
A
A set
those which give the least calories are the most preferred; and so on.
Years ago, any advocacy of L-orderings was commonly criticized since
such orderings cannot be represented by a utility function [see Georgescu-
Roegen 1954; Newman 1965; Quirk and Saposnik 1968, Chapter 1]. Rarely
today are such orderings mentioned and this, of course, is quite apart from
Z
the lingering suspicion of some economists that the consumer™s process of
deciding on an optimum choice is better presented by an L-ordering. The
X
commonplace rejection of L-orderings on purely methodological grounds XA
may be a mistake based on a confusion concerning what L-orderings are Figure 12.1 A lexicographic ordering
and how they differ from the existence of multiple criteria. If there is a
confusion here it needs to be cleared up and a good starting place would be
© LAWRENCE A. BOLAND
168 Principles of economics Lexicographic orderings 169
bundle with more of good X to any bundle with less X regardless of the the utility, the real numbers used for the index of the utility (or of the
quantity of Y in either bundle, and if (and only if) the two bundles being implied ranking) turns out to be insufficient. If we assign a real number for
compared have the same quantity of X, then those bundles which have every point in the X“Y space, there will not be enough numbers. For
more Y will be preferred. For purposes of illustration let us assume points example, all those bundles which have the same quantity of X as point A,
have thickness such that the consumer™s ordering looks like Figure 12.1. that is, XA, will be represented by the same number, namely X A, even
Here there is only one point on the boundary between the ˜worse than™ and though the consumer has ranked a sub-set of them according to the quantity
the ˜better than™ set, namely A, the point in question. One problem is that of Y. That is, there exist an infinity of points for which there does in fact
for a continuous set represented by any positively sloped line which does exist an ordering, but they all appear to be of equal rank since they have X A
as the index of utility. 1 This ˜discontinuity™ problem can also arise for more
not pass through point A, such as Z“Z¢ in Figure 12.1, whenever we attempt
to represent the consumer™s preference ordering with an ordinary utility sophisticated L-orderings [see Georgescu-Roegen 1954]. The formal
function there is a jump in the utility index as we ˜move™ along Z“Z¢ across problem here is that we can never use one of the multiple criteria of any
the boundary between bundles with less and more X than point A. This is L-ordering as an index for the effect of the entire ordering on the space
because all bundles with the same amount of X but with a different amount which represents all conceivable bundles of goods.
of Y will have a different utility index value. Those points on the vertical Neoclassical theorists reject L-orderings as a form of the utility function
line above A have a higher index than those below A. The result is such that typically assumed in the theory of demand. This rejection of L-orderings
does not seem to recognize the question of the process by which a
Utility consumer determines the best bundle and it is not clear that the neoclassical
concept of a utility function is adequate for that purpose.
U(X,Y)
ORDERINGS AND CONSTRAINED MAXIMIZATION
Before considering multiple criteria as a basis for an explanation of the
choice process, let us examine the only accepted way to use multiple
UA criteria in neoclassical demand theory. In the case of constrained
maximization, the choice of a best bundle involves two orderings: the
unobservable preference ordering that is usually represented by an
indifference map and the observable expense ordering as represented by the
family of parallel budget lines where each budget line represents a different
dollar value. Clearly an expense ordering by itself is insufficient to explain
a consumer™s unique choice since there are many points along the budget
Z′
Z line which (by definition of that line) are ranked equally (i.e. they cost the
Figure 12.2 Utility along Z“Z¢ line same). Why does the consumer choose one rather than another? The
consumer is thus thought to use these two orderings in a two-step manner.
there is no point with the same utility as A. In Figure 12.2 this situation is The consumer is thought to narrow the choice to the chosen bundle by first
represented by a utility function which assigns different levels of utility for excluding all those points which he or she cannot afford (i.e. points beyond
each point on the Z“Z¢ line. Here all bundles on the Z“Z¢ line to the left of the given budget line) and second picking the best point among those that
are affordable according to the preference ordering. 2 This is not really a
point A have a lower level of utility and all bundles to the right have a
higher level. There is, however, a discontinuity since all bundles with the choice process since it is more a ˜static™ choice which only requires that the
same quantity of good X but different amounts of Y have to have a different individual be able to find the optimum bundle by correctly calculating
level of utility. This discontinuity may not be considered a serious problem utility levels for each point along the budget line.
but the following type of discontinuity always is. Whether we can correctly represent the consumer™s choice this way
When we directly use the quantity of good X as a proxy for the index of depends on what we assume about the unobservable preference ordering.
© LAWRENCE A. BOLAND
170 Principles of economics Lexicographic orderings 171

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