Formalization of the Context "Satisfaction"

Claudio Gutierrez

As a conclusion which can be drawn from the general discussion, we can say that the concept of substitution is common to the traditional theories of value and also to the attempts to build a definition of economics. NOTE 1 That concept comes to the foreground only in the formal approach, whereas it tends to remain in the background in the traditional ones. For the objective theory of value is based on the cost of production of goods, but makes sufficient and essential use of the concept of exchange-value. So does the subjective theory, although it is founded on the concept of individual satisfaction of wants. On the other hand, the classificatory definition of economics puts main emphasis on the causes of material welfare, although it also stresses the phenomena of exchange related to the intervention of money. Similarly, the analytical definition, for instance in Robbins' formulation, NOTE 2 mentions scarcity of means and also makes use of the concept of alternative application of resources. Contrasting the utility conception with the formal conception, we have: Utility theory is normally expressed in terms of subjective satisfaction and, secondarily but essentially, in terms of exchange (substitution). The analytical definition is expressed in terms of scarcity and of alternative uses (substitution). The formal conception expresses itself only in terms of substitution, the semantic and pragmatic "sense of direction" of the system being best confined to the informal context of the theory. NOTE 3 Two consequences follow from here. First, that greater generality is accomplished with the modified view, since the theory of value itself can serve to identify the economic subject-matter, without the interposition of a–not necessarily fruitful–strict definition of economics. NOTE 4 Second, the defense of the formal approach must clarify the role of the key concepts "scarcity" and "satisfaction," and show that their presence in the formal theory of value can be confined to the token necessary to represent within the formal picture the empirical openness of the system. The attempt to meet this challenge will be the content of the remainder of this chapter. It will consist of two steps. First, to construe value analysis without including "satisfaction" operatively within the model. Second, to construe the description of economic analysis without making independent reference to "scarcity".

That value analysis could be construed as the operation of a model not including the concept of "satisfaction" can be shown in two different ways. Both have in common the same strategy of proof: to point to some consecrated, time- honored, use of the term "utility" or "value" in a sense not defined with the help of the concept of "satisfaction," and to offer a demonstration as to how such use can be generalized so that it covers the ground commonly governed by the sense of "utility" or "value" defined in terms of "satisfaction". The first argument is going to draw from the use of "utility" in the field of producers' goods. The second, from the use of "utility" in monetary theory.

My first argument is this. As it is shown in the following quotation, there is a consecrated use of "utility" that makes no mention of satisfaction but rather uses the more concrete idea of maximization of monetary receipts, namely, the utility of producers' goods.

The utility which a businessman derives from the things which he buys for business purposes is the extra receipts which he obtains thereby . . . . (HENDERSON 63, p. 40)

Now, one can alternatively consider both the business man and the consumer trying to maximize his money holdings. The latter, of course, not by producing commodities but by preserving them or, more generally, by saving the means to buy them–purchasing power. There is no reason in principle why this conception of utility could not suffice to render, from the point of view of model construction, all phenomena of maximization, including those corresponding to consumers' goods. NOTE 5 The practical problems the consumer has to solve in order to maximize are, of course, different from the practical problems the producer or businessman has to solve. Nevertheless, they are formally homologous. The businessman may be interpreted as trying to save the most money which comes to him as a result of exchange processes of the inevitable leakage represented by the cost of production–the hard facts of technology! The consumer, on the other hand, may be interpreted as trying to keep the most of the money that comes to him as a result of exchange processes, in spite of the inevitable leakage represented by the necessities of living or pleasurable expenditure–the hard, or sweet, facts of life! In both cases, of course, allowance must be made for the contrary operation to leakage, which we could call "injection," NOTE 6 result of sheer chance, industry and the providence of nature. "Leakage" and "injection" will have in common their not being results of exchange, and so of being somehow external to the model.

My second argument is this. As it is clear from the following quotations, there also exists a professional use of "utility" which makes no direct use of the term "satisfaction" either, namely, the concept as applied in the macroscopic field to the medium of exchange itself, that is, money. To wit:

We shall have to examine more carefully in a moment what we mean by this phrase "the value of money"; for the present we may define it provisionally as the power of money to purchase the things people want. . . . (ROBERTSON 64, pp. 8,9)

Let us notice first that the reference to satisfaction ("the things people want") is not essential to the definition, which can be rendered as "the power of money to purchase other things". When the promised, more careful examination comes, moreover, the matter is set in such a way that it points to the formal extension of this sense of "utility" or "value" to the whole economic domain:

By the value of money we mean something exactly analogous to what we mean by the value of anything else, say bread or cloth: that is to say, we mean the amount of things in general which will be given in exchange for a unit of money. . . . (ROBERTSON 64, p. 14)

Again, I can see no systematic reason why one could not extend this use of "utility," i.e., the concept of value as all the things which can be bought by the marginal unit, to all commodities other than money. If it is true that "money cannot be eaten," this obstacle does not seem insurmountable from the formal point of view, which is the one suitable for the analysis of a formal apparatus. For one thing, the macro and the micro concepts of utility are essentially connected in the fact that prices of anything equal marginal utility as measured in terms of money, i.e., relative to the marginal utility of money to the purchaser. If one takes the substitutability of one thing for all other things as central, there is no reason to consider the two examples of substitution-things for money, things for thing-as fundamentally different. One can argue that this twist condemns the concept of value to hopeless circularity. Yes, but it is a virtuous rather than a vicious circularity, a circularity of the kind that makes all formalism capable of adequate operation. It is saved from meaninglessness by the interpretation in toto of the formal system at the pragmatic level of the science. Secondly, the impossibility of consumption that seems to be the exclusive characteristic of money tends to be not that exclusive under a purely modelic interpretation of "consumption" as leakage from a closed system where everything is considered an object of study while it remains within the system. It is another question whether this conception is artificial or unfruitful, but it is difficult to see how one could say that it is not consistent and operative. One could even turn the tables around and say that the "consumption" of money in the case of the miser or other similar cases (the collector) does in fact equalize the cases of the macro and the micro economy. The fact that the "consumption" on one case is more abundant than in the other does not essentially change the picture.

The "macro-micro" argument is especially important because it contributes to the emphasis of the formal character of models in economic analysis. Thus, money is the most formal of all commodities because it is in normal circumstances the most substitutable, consisting of the medium of exchange itself. But all other commodities, precisely to the extent that they are commodities-goods produced under a system of exchange-are also formal in the same sense, although to a different degree. They are also capable of conception under relations of substitutability. Money represents in an ideal or perfect way the unity of the system of substitution. But all other commodities do also in fact represent the same unity, much as the monads of the Leibnizian world were said to reflect the whole universe. Hence, we are entitled to say that they have value because of the same reason money has value, namely because they can exchange for other things. So, for both money and all other commodities one can define their value as the alternative sum of all the other things that can be bought by the marginal unit of the particular commodity, be it money or anything else. The most noticeable difference between the two cases, which is no disproof of the feasibility of the unitarian conception of utility, is that money is less committed to "get out" of the system. It tends to remain longer within than do the goods it buys. Those are, of course, and by hypothesis, on their "way out" of the system. On the other hand, money is always in danger of disappearing wholesale from the system by monetary reform. An investigation of this difference, without impairing the formal conception of value, could lead to the development of the different chapters of economic theory: the theory of prices, the theory of money, and even the theory of cycles. NOTE 7

The conception of economic theory in terms of relations of substitutability, however, must not obscure the fact that a solution for the equilibrium system is always needed. This is why my first argument is important; the fundamental homogeneity of utility of producers and utility of consumers point to the essential role of (quantitative) maximization for the determination of a system of substitution. This need of determination, which seems to be a clear case of the general requirement of logical closure of a theoretical system, does not alter the formal or syntactic character of the system. The interpretation of the equilibrium point may run in terms of "satisfaction"; but in itself it is capable of being understood as the simultaneous determination of all the functions involved in a particular problem.

We still have to come to grips with the major objection of artificiality. Is it not artificial, and hence unfruitful, to present the bulk of economic theory as something having nothing to do with the very reason for the existence of economic activity, namely the satisfaction of individual wants and desires? My answer to this is that in fact it is artificial, in the sense in which all symbolic processes, but most especially the formal ones, are artificial. Is not the very invention of money as a representation of the indefinite mass of goods artificial in the same sense? As a matter of fact, a similar charge of artificiality or unnaturalness has been made against practically every kind of formalism or mechanical device which, in the end, has turned out to be very beneficial to mankind. In particular, I am thinking of the ways and methods of modern science and technology. Now, the chances of a given mechanism being a blessing rather than a curse are enhanced rather than diminished by an adequate understanding of its real nature and of the principles on which it rests. Ignoring them can only result in bad performance of the machine, in tragic misunderstanding of its purposes, and eventually in self-fulfillment of the omen that branded artificially as inhumane in the first place.