Garcia de la Sienra The Modal Laws of Economics

Philosophia Reformata 63 (1998) 182–205

THE MODAL LAWS OF ECONOMICS

Adolfo García de la Sienra

0. Introduction

Herman Dooyeweerd’s classical characterization of the mean-ing-kernel of the economic modality runs as follows:

the sparing or frugal mode of administering scarce goods, implying an alternative choice of their destination with regard to the satisfaction of different human needs.1

My first aim in this paper is to show that Dooyeweerd’s char-acterization of the meaning-kernel of the economic modality natu-rally leads to neoclassical economic theory. In order to do this, I will provide an argument that, departing from Dooyeweerd’s definition of the meaning-kernel of the economic modality, concludes in a logical reconstruction of (the static case of) neoclassical economic theory (from now on denoted as NET). The fundamental law of this theory will turn out to be thus, naturally, a formulation of the fundamental modal law of economics. The second aim of the paper is epistemological since it discusses the methodological problem of the empirical claim of the theory. It is my hope that this discussion will clarify the limits of NET and provide a reply to the objections raised against it by Reformed scholars like Goudzwaard (1980).

1. Economics as the Theory of Efficiency

Since Dooyeweerd was not an economist, his aim in describing the meaning-kernel of the economic modality was not to build a new economic theory, but rather to capture the substance of what it means to be economic. I think that his insight is quite deep, indeed, and strikingly similar to the prevailing conception of the economic as developed by Lionel Robbins in an influential book written by the time when Dooyeweerd was producing his De wijsbegeerte der wetsidee (1935-6).2

1 Dooyeweerd (1984), v. 2, p. 66. 2 Robbins’ book was published for the first time in 1932, but it is quoted

the modal laws of economics 183

First of all, Robbins distinguishes a classificatory conception of economics from an analytical one. An analytical conception

does not attempt to pick certain kinds of behaviour, but focuses attention on a particular aspect of behaviour, the form imposed by the influence of scarcity. It follows from this, therefore, that in so far as it presents this aspect, any kind of human behaviour falls within the scope of economic generalisations.3

In focusing its attention on a particular aspect of behavior, the analytical conception agrees with Dooyeweerd’s contention that man is able to subject himself to economic laws: insofar as a human behavior is subjected to economic laws, that behavior displays properties belonging to the economic modality, which is to say that the behavior exhibits an economic aspect. Hence, there is a methodological point of contact between the view of Dooyeweerd and that of Robbins. Yet, the philosophy of the law-idea (from now on WdW) claims that the analytical conception must be complemented with a classificatory one, because some behaviors—specifically some forms of organized behavior—can be seen as qualified by economic laws, which means that they are of an economic kind, even though this is not to say that they do not display properties belonging to other modalities. I shall call ‘economic behavior’ any behavior qualified by economic laws. The logical analysis of Dooyeweerd’s compact definition of the economic meaning-kernel clearly reveals four universal components in the economic aspect of any economic behavior:

(D1) Human needs. (D2) Scarce resources. (D3) An alternative choice of their destination with regard to the

satisfaction of the human needs. (D4) A frugal or efficient choice regarding this destination.

This implies that any agent placed in the Land of Cockaigne cannot display economic behavior. Certainly, such an agent may have needs, but there is no scarcity and therefore does not to have to economize, i.e. to make an efficient use of resources. There are many situations in real life where there is plenty of some factor and so the agent does not think he has to make an efficient use of it. The neither in De wijsbegeerte der wetsidee nor in A New Critique of Theoretical Thought (which is a more recent, revised and enhanced edition of the former work). Hence, it is quite sure that Dooyeweerd never read it.

3 Robbins (1984), pp. 16-7.

184 adolfo garcía de la sienra

reference of the term ‘human needs’ is relative, in the sense that it varies from one situation to another and also from one agent to another. We shall deal with this relativity later, when we discuss the intended applications of NET. Yet, it can be made precise when a particular, concrete economic behavior is being discussed. These needs are reflected in the preferences of the agent. For instance, if in asking an agent he says that prefers beans over parfums, we may gather that he feels more need of eating than of smelling well. Examples like this, which are quite abundant, make clear that the concept of preference is unavoidable, natural, and useful to characterize the concept of a human need: all of the time we can see ourselves and other people preferring one thing over another. This does not mean that preferences are necessarily “rational” (i.e. connected and transitive), only that the concept is of wide applicability and indeed necessary when it comes to the description of economic behavior. The concept of scarce resources, on the other hand, is relative to proposed ends. There are no scarce resources in themselves but only with respect to some purpose. And the ends may also conflict among themselves, in the sense that reaching one end may preclude the reaching of another. When the resources available to an agent are sufficient to reach all his ends, there is no problem of scarcity, but then no economic behavior either. The fact of scarcity forces the agent into ordering his ends and making an efficient use of his resources, since in this form he can obtain the realization of more ends. In other words, the agent is forced into producing preference rankings of his ends and making optimal (or “good”) use of resources to achieve as many ends as possible with the resources available. Hence, we see that Dooyeweerd’s definition of the meaning-kernel of the economic modality leads us in a very smooth way into the concept of preference-maximization. One of the clearest formu-lations of economics as the study of preference-maximization is due to Robbins in the book mentioned above. In what follows, I will compare in some detail his view with that of Dooyeweerd. According to Robbins, what makes economic an aspect of human behavior?

Analyzing first the case of a “Robinson Crusoe”, Robbins says that the answer to this question is to be found in four conditions:4

4 Robbins (1984), p. 12.


(1) Isolated man wants both real income and leisure. (2) He has not enough of either fully to satisfy his want of each. (3) He can spend his time in augmenting his real income or he can spend it in taking more leisure. (4) It may be presumed that, save in most exceptional cases, his

want for the different constituents of real income and leisure will be different.

There is no doubt that the behavior of isolated man is a possible, interesting case of behavior, and I do not see any reason why Dooyeweerd or a philosopher of the law-idea should shun it. But we shall see that Robbin’s former description accurately expresses the meaning-kernel of the economic modality as Dooyeweerd described it. Condition (1) is very likely to express the dilemma of a Robinson Crusoe, since man needs both resources to reproduce his existence and rest. Condition (2) is fulfilled in every land but Cockaigne’s. Even in a tropical island man has to fish, hunt, collect and build a roof against the rain (or hurricanes!). Hence, (3) Crusoe is faced with the need to determine how much time he must devote to work, and how much time to leisure and rest. Also, it is but common sense and pretheoretical experience that man prefers more of one thing than of another; certainly, Crusoe may like (say) grilled fish more than raw crab. In more general terms, given these conditions, the isolated man has to economize because he has to choose between different wants: if he chooses more leisure time, he will have less real income, and viceversa. Robbins finds precisely in this relationship, between the disposition of his time and his system of wants, the properly economic aspect of his behavior. The problem is that the time and means for achieving the ends of the isolated man are limited and capable of alternative application. The Robinson exercise is but the elaboration of an example where four “fundamental characteristics” of the economic aspect of human behavior are found, to wit:5

(R1) The ends are various. (R2) The time and the means for achieving these ends are limited.

5 Robbins (1984), p. 12.


(R3) The time and the means for achieving these ends are capable of alternative application.

(R4) The ends have different importance. These conditions of human existence make some human acts have an economic aspect:

when time and the means for achieving ends are limited and capable of alternative application, and the ends are capable of being distinguished in order of importance, then behavior necessarily assumes the form of choice. Every act which involves time and scarce means for the achievement of one end involves the relinquishment of their use for the achievement of other. It has an economic aspect.6

It is easy to see that there is almost a one-to-one correspondence between (D1)-(D4) and (R1)-(R4). What Dooyeweerd calls ‘human needs’ correspond to Robbins’ ends; Dooyeweerd’s scarce resources are Robbins’ limited means; Dooyeweerd’s alternative destination of means correspond to Robbins’ alternative application of the means. Dooyeweerd’s frugality or efficiency is nothing but Robbins’efficient use of the means on the basis of the different importance of the ends, namely, directing the means to fulfill those ends which are ranked as most important for the agent. This is precisely what is called ‘preference-maximization’ in the literature. Hence, it is clear that Dooyeweerd’s characterization of the economic kernel is quite akin to the neoclassical view of what economics is.

2. A Science-Theoretic Apparatus

Dooyeweerd’s and Robbins’ shared view of the meaning-kernel of the economic modality (i.e. of the nature of the economic aspect of human behavior) naturally leads to the conceptual apparatus of neoclassical economic theory. In order to formulate NET in a perspicuous way, a way that clearly displays the fundamental law of the theory, but above all the empirical claim, I shall follow the structuralist metatheory as expounded in Balzer, Moulines and Sneed (1987). An empirical scientific theory can be represented as a net of theory-elements dominated by a fundamental one, called the basic

6 Robbins (1984), p. 14.


theory-element: all other theory-elements in the net turn out to be special cases of the basic one. Roughly, the basic theory-element “is” the fundamental law of the theory, but actually there is much more to a theory-element than merely a law. The cornerstone of the structuralistic metatheory (from now on SM) is the notion of a structure. This notion was developed mainly by Bourbaki (1968) but applied for the first time to the empirical sciences by Patrick Suppes. Some (if not all) empirical scientific theories can be axiomatized through the definition of a set-theoretic or Suppes predicate. For instance, a complete axiomatization of classical particle mechanics by means of a Suppes predicate runs as follows. DEFINITION 1: � = (P, T, s, m, f) is a system of classical particle mechanics if the following axioms hold, for every p in P and t � T:

(1) P is a nonempty set; (2) T is a closed interval of real numbers; (3) s: P ∞ T ∅ R3 is a vector-valued function such that d2s(p,t)/dt2

exists; (4) m: P ∅ R+ is a real-valued function that assumes only positive

values; (5) f: P ∞ T ∞ N ∅ R3 is a vector-valued function such that the

series ℜ i � Ν f(p,t,i) is absolutely convergent;

(6) f (p,t,i ) = m(p) ⋅i∈Ν∑

d2sdt 2

A quick glance at this system of axioms reveals two well defined groups of sentences. Axioms (1)-(5) merely characterize the type of the set-theoretic objects P, T, m, s and f. Thus P, to be interpreted as a set of material particles, is characterized merely as a nonempty set from a set-theoretical viewpoint. T is characterized as an interval of real numbers to be interpreted as instants of time. s is the position function, that assigns to each particle at every instance a position; i.e. a point in three-dimensional Cartesian space, designated with respect to a non-inertial reference frame. m is the mass function, assigning a positive real number to each particle, designated with respect to a system of measurement units. f, finally, is the force function; f(p,t,i) is a three-dimensional vector that represents the ith force (with respect to the same system of measurement units and reference frame) to


which particle p is subjected at time t (in all mechanical problems, all but a finite number of the terms ‘f(p,t,i)’ are assumed to be zero). On the other hand, (5) is a law of the theory properly speaking—namely

Newton’s second law. It turns out that sentences of the first kind—characterizations —can be defined in the following, rather simple way. A sentence ϕ is a characterization iff ϕ contains, besides set-theoretic symbols and symbols for basic sets (universes of discourse), only symbols for precisely one relation.7 Suppose T is a theory formulated by means of a Suppes predicate. The class of all structures satisfying the characterizations will be called potential models of T and denoted as Mp(T). The models of T (M(T)) will be the potential models which, in addition, satisfy the proper axioms of the theory; thus M(T) ⊆ Mp(T). Among the primitive terms of a theory some terms can be distinguished that can only be determined if a certain application of the theory is assumed to be succesful. For instance, in classical mechanics you cannot determine the mass (or weight) of a body without using a balance (say). But then the actual measurement of the mass is really meaningful (“true”) iff the balance itself is correctly seen as a case of a mechanical system, as a succesful application of the theory. Terms of this type have been called T-theoretical by SM. In other words, that a given term is T-theoretical means that it can be determined only if T’s fundamental laws are presupposed as holding in certain cases.8 But perhaps the crucial fact about theoretical terms is that they are the explanatory factors in any theory. For instance, in classical mechanics mass and force are the terms by means of which the described motion of the bodies is explained. We shall see that something analogous happens in NET, where utility is the factor by means of which the behavior of the economic agents is to be explained. Thus, in any potential model (X1, ..., Xk, Y1, ..., Ym) of a theory T we shall distinguish among the objects Y1, ..., Ym those that are T-theoretic from those that are not. For l ≤ m, we shall let Y1, ..., Yl

7 For a thorough discussion of this issue, see Balzer, Moulines and Sneed

(1987), pp. 13 and 14. 8 For a very complete and lengthy discussion of theoreticity, including precise

definitions of this notion, the reader is referred to Balzer, Moulines and Sneed (1987), pp. 47-78.


be the T-non-theoretical terms and, accordingly, Yl+1, ..., Ym shall be the T-theoretical ones. When l = m we say that all objects are T-non-theoretical. Let Mpp(T) = {(X1, ..., Xk, Y1, ..., Yl) Ω (X1, ..., Xk, Y1, ..., Yl, Yl+1, ..., Ym) � Mp(T)} be the family of all structures that result from those in Mp(T) when their theoretical components are removed. This is the class of the partial potential models of theory T. The “removal operation” can be represented by means of a surjective function r: Mp(T) → Mpp(T), such that r(X1, ..., Xk, Y1, ..., Yl, Yl+1, ..., Ym) = (X1, ..., Xk, Y1, ..., Yl). It follows that r(M( T)) ⊆ Mpp(T). Usually, a theory is applied to concrete, bounded phenomena. For instance, classical mechanics is applied to a system consisting of the sun and one planet, or to one body in free fall (i.e. the earth and that body). These systems are considered as “relatively closed”, in the sense that the influence of their environment is neglected.9 Yet, these local applications can overlap in space and time, may influence each other, and certain properties of the objects may remain the same if transferred from one application to the other. These connections are captured by SM by means of constraints. Formally, a constraint is a family C of sets of potential models representing certain admissible combinations among these models. It suffices here to point out that a constraint C for a theory T is a subset of the power set Po(Mp(T)) that has the following properties: (1) C ≠ Ø; (2) Ø ∉ C; (3) for all � ∈ Mp: {� } ∈ C.10 DEFINITION 2: A theory-element core K, of a theory T formulated by means of a Suppes predicate, is a structure of the form (Mp, Mpp, r, M, C) such that

(1) Mp is the set of potential models of T; (2) Mpp is the set of partial potential models of T; (3) r: Mp → Mpp is such that

r(X1, ..., Xk, Y1, ..., Yl, Yl+1, ..., Ym) =(X1, ..., Xk, Y1, ..., Yl).

(4) M ⊆ Mp; (5) C is a constraint for Mp.

9 I shall return to this when I discuss Goudzwaard’s criticism of NET’s supposed

causal closure of economic phenomena. 10 For a thorough motivation and discussion of the philosophical meaning of

these conditions, the reader is referred to Balzer, Moulines and Sneed (1987), pp. 40-47.


A theory consists not only of the theory-element core, but also of a domain of intended applications I, which is a pragmatically and historically determined subset of Mpp. This set I is usually taken to be the “observational” part of the theory, but this can be misleading. For example, Tycho Brahe’s huge compilation of observations of the motions of Venus yields a finite structure of data � that suggests a description of that motion by means of a continuous (and therefore nondenumerable) function whose image looks like an ellipse. This last function gives rise to a structure ı in I. (Recall that in mechanics all elements of I describe the motion of bodies by means of twice-differentiable functions of time.) Hence, as an example of I, think of all the kinematical descriptions of the motions of bodies that Newtonian theory was supposed to apply to: orbits of planets, the Huygens pendula, armonic oscillators, free-falling bodies, and so on. I shall distinguish, accordingly, the family of data structures D from the domain of intended applications. I may define the most fundamental unit constituting a scientific theory as follows. DEFINITION 3: A theory-element is a pair (K, I) such that K is a theory-element core and I ⊆ Mpp. The empirical content of theory T is the family of all partial potential models of T that can be extended (by means of suitable theoretical components) to models of T whose theoretical compo-nents satisfy the constraint C. I shall let Cn(K) denote the empirical content of T, i.e. the set Cn(K) = r(Po(M) ∩ C) = {E ∈ Po(Mpp) Ω For every � ∈ E there is an F ∈ Po(M) ∩ C and a ı ∈ F such that � = r(ı)}. Thus, the empirical claim of the theory is that I belongs to Cn(K). The relation between a data structure � ∈ D and an inten-ded application ı ∈ I properly conceptualizing it can be depicted as an imbedding i: � → ı, since both structures are of the same similarity type; the question whether there is such an imbedding for a given data structure is also an empirical matter. Informally, by a theory I have meant a conceptual structure that can be formulated by means of a Suppes predicate. Actually, as I said at the beginning of this section, a scientific theory is more complicated than this: It is more accurate to say that it is a net of theories in the previous sense, dominated by a basic theory-element and related by a specialization relation. Roughly, for every theory there is a basic theory-element and all the other theory-elements are


but specializations of the first one. For instance, the basic theory-element of classical particle mechanics contains as a proper axiom only the fundamental Newton’s second law (F = ma). A specialization of this theory-element is celestial mechanics, which includes additional parameters and special laws (like the law of universal gravitation: F = G(m1 ⋅ m2)/r2). Other specializations contain other laws and other special parameters. 11 Naturally, a specialization of a theory-element narrows down the original set of models, constraints and intended applications, and so it can be defined in the following terms. DEFINITION 4: If T = (Mp, Mpp, r, M, C, I) and Tæ = ( Mæp, Mæpp, ræ, Mæ, Cæ, Iæ are theory-elements, then Tæ is a specialization of T iff

(1) Mæpp = Mpp; (2) Mæp = Mp; (3) ræ = r; (4) Mæ ⊆ M; (5) Cæ ⊆ C; (6) Iæ ⊆ I.

Finally, I can properly define a (scientific) theory as a set of theory-elements, partiallly ordered by the specialization relation, that has a maximal element called its basic theory-element. We shall see in what follows how can NET be reconstructed by means of this metatheory.

3. NET as the Theory of Frugality

NET can be reconstructed as a specialization of game theory, namely the case in which the strategy of any personal player cannot affect those of the others or the states of nature. Usually, nature is interpreted as “the market”, and the states of nature as prices or a combination of prices and endowments of wealth for the personal players.12 Robinson’s situation as an isolated man is a special case of economic behavior, but it is more interesting and usual for NET to

11 For a thorough reconstruction of the important case of classical particle mechanics and its specializations, see Balzer and Moulines (1981).

12 For a thorough discussion of the logical structure of games in extensive form, see García de la Sienra (forthcoming).


study the coordinate behavior of several small agents acting simultaneously. In order to study the economic aspect of a given situation in which n personal agents are taking decisions, NET represents the space of possible actions of agent i ⊆ I = {1, ..., n} by means of a certain nonempty set Ai. Nature or the market is represented by set A0, and the family of all players, be it nature or personal, is J = I ∪ {0}. If a = (a0, a1, ..., an) is a system of possible actions and state of nature, a point in A = ∏ j � J Aj, I shall denote with a-j the vector (a0, a1, ..., aj-1, aj+1, ..., an). Thus, if I am allowed a slight notational abuse, I will write vector a as (a-j, aj). Sometimes, for notational convenience, it is said that agent j � I faces actions or states of nature a; this means that he faces a-j. When nature or agents other than personal agent j adopt deci-sions or yield states a-j, the space of possible actions for j is restricted to feasibility set ϕ j(a-j, aj) ⊆ Aj. Agent j is then constrained to adopt an action in this feasibility set, a point d(j, (a-j, aj)) in ϕ i(a-i, ai). Every agent i � I is assumed to have a utility function ui defined over his set of possible actions Ai. The characterizations of these terms yield the class of potential models of NET. As usual, I omit the auxiliary sets (I, J and R at the present time) in the definition. DEFINITION 5: � = (A0, A1, ..., An, ϕ 1, ..., ϕ n, d, u1, ..., un) � Mp(NET) iff for every i � I and j � J:

(1) Aj is a nonempty set; (2) ϕ : A → Ai is a correspondence not depending upon the

ith variable, so that ϕ j (a-j, aj) = ϕ i(a-j, ajæ for every aj, ajæ � Ai with j = i;

(3) d: I ∞ A → Ai is a function; (4) ui: Ai → R is a function.

Characterizations also have an intended empirical meaning. The empirical meaning of axioms (1)-(4) is the following.

(E1) Every agent can perform some action and nature present a state. (E2) The actions that an agent can actually perform depend upon the

actions performed by the other agents, as well as the current state of nature.

(E3) Every agent decides to perform some action given any system of actions by the other agents and state of nature.

(E4) Every personal agent has a utility function over his set of possible actions.


Conditions (E1)-(E4) provide a heuristic guide to the application of NET in given empirical situations. This does not mean that all terms introduced in Definition 5 are on the same theoretical level. Typically, NET’s normal scientists assume that terms Ai, ϕ i and d provide the “empirical” or “observational” part of the theory, whereas utility is a “non-observable” magnitude which is supposed to be the “causal factor” in the explanations provided by NET. Indeed---as I will show below---the typical method of determination of utility presupposes that the fundamental law of NET is already holding in some empirical situation. As I suggested when discussing the notion of a theoretical term above, this type of circularity is not anomalous in scientific theories, but rather normal. Hence, the partial potential models of NET are structures of the form (A0, A1,..., An,ϕ 1, ...,ϕ n, d). A typical data structure is a structure of this type where d is a (finite) function describing the actual behavior of the agents. For every agent i � I, we can define the set of all actions available to agent i that maximize his utility given that the other agents adopted actions (a0, a-i). DEFINITION 6: The set of optimal actions for agent i � I given actions a is

mi(a) = {b � ϕ i (a) Ω ui(b) = max ui(c)}. cefi(a) For any a � A, let m(a) = m1(a) ∞ ... ∞ mn(a). The fundamental law of NET asserts that, in fact, there is some utility function ui (i � I) for each agent, such that every action performed by any agent maximizes his corresponding utility function. This law is the very core of the basic theory-element of NET. DEFINITION 7: � = (A0, A1, ..., An,ϕ 1,..., ϕ n, d,u1, ..., un) � M(NET) iff � � Mp(NET) and the following axiom holds for every i � I and a � A:

d(i, a) � mi (a) (Fundamental Law) In order to discuss by means of a particular example the role of utility in NET, as well as a specific method of determination of utility,


I shall consider a very important specialization of the basic theory-element: the classical theory of Walrasian demand. There is only one set of actions in this specialization: A1 is a set of non-negative vectors representing amounts of L types of goods; actually A1 = R +

L , the nonnegative orthant of the usual Euclidean space of L dimensions. A0 is a set of positive vectors, actually the interior (R +

L+1 )° of R +L+1 , representing systems of prices and wealths,

(p, w). The feasibility correspondence for the only personal agent, ϕ 1, is denoted by B and assigns a budget set Bp,w = {x � R +

L Ω px ≤ w} to every pair (p, w) of price and wealth. The choice or decision function d is denoted by x. Bp,w is called the Walrasian budget set and x(p, w) the Walrasian demand function. Hence, the classical theory of Walrasian demand (WD) is a specialization of NET, as the following definition makes evident. DEFINITION 8: ((R +

L+1 )°, R +L , B, x, u) � M(DW) iff ∃ (A0, A1, ϕ 1, d,

u1) � M(NET) such that R +L = A1, (R +

L+1 )° = A0, B = ϕ 1, x = d, u = u1, and the following axioms hold:

(1) ∀(p, w) � (R +L+1 )°: Bp,w = {x � R +

L Ω px ≤ w }; (2) x is differentiable; (3) (Walras’ Law) ∀(p, w) � (R +

L+1 )°: px(p, w) = w; (4) (Homogeneity of Degree Zero) ∀(p, w) � (R +

L+1 )°,∀a � R+: x(ap, aw) = ax(p, w); (5) u is a continuous function, representing a locally non-

satiated and strictly convex preference relation over R +L .

The fundamental problem of NET (in particular, of DW), as of any empirical theory, is to explain the observational data by means of its theoretical concepts. In the language of SM, these data are represented by a data structure � = ((R +

L+1 )°, R +L , \O(B,ˆ), \O(x,ˆ)) � D,

where the correspondences or functions \O(B,ˆ) and \O(x,ˆ) are finite and discrete. The explanation begins when � is imbedded into a partial potential model of DE, a structure ı = ((R +

L+1 )°, R +L , B, x) of

the same similarity type as � , that satisfies axioms (D8)(1)-(4). In such a case, the problem boils down to find a utility function u such that � = ((R +

L+1 )°, R +L , B, x, u) � M(DW) and ı = r(� ).

It does not make any sense to try to determine the utility functions associated to an “observed” demand function if these functions do


not exist. The existence of these functions is warranted whenever the demand function has certain properties. Now, the fact that only some points of the demand function can actually be observed, and all the other are observable “in principle”, entails that any property about all possible observations is itself non-observable. Hence, the conditions upon the demand function (on the partial potential models) guaranteeing the existence of utility functions “rationalizing” the demand function are a petitio principii, a roundabout way of assuming that the demand function is actually rationalizable. But, as I said above, this kind of circularity is typical of empirical science and necessary to determine the theoretical terms of a theory. There is a general result, due to Houthakker (1950) and Richter (1966), according to which the Strong Axiom of Revealed Preference is necessary and sufficient for rationalizating a demand function.13 But this result is not constructive, since it does not tell us how to obtain the actual utility function. A typical utility-determination method is the following.14 In order to obey the Fundamental Law of NET (Definition 7), the agent has to “solve” the following problem for any pair (p, w) given to him:

maxx � 0 u(x), subject to px � w. For given p and utility level u, the dual of this problem is

minx � 0 px, subject to u(x) � u. By axioms (2) and (5) of Definition 8, the function e: R+° ∞ R+ → R, that assigns to every pair (p, u) the solution to this last problem, is homogeneous of degree one, concave and differentiable in p, and strictly increasing in u.15 This implies that e(p, u) = min {pxΩ x � Vu }, where Vu is the level set

13 We say that the demand function x satisfies the Strong Axiom iff for any N � N

and any sequence (p1, w1), ... (pN, wN) in (R +L+1 )°: pn x(pn+1, wn+1) ≤ wn for every

n ≤ N implies pNx(p1, w1)> wN; i.e. if for every n ≤ N menu x(pn, wn) is revealed as preferred to menu x(pn+1, wn+1) (this last menu is affordable at prices and wealth (pn, wn), but the former is actually chosen) then menu x(p1, w1) is not chosen at prices and wealth (pN, wN) only because it is not affordable at such prices.

14 See the details of this method in Mas-Collel et al. (1995). 15 See Mas-Collel et al. (1995), pp. 59 and 78.


Vu = {x � R +L Ω px � e(p, u) for all p > 0}.

The required preference relation is obtained by condition

x \O(>,~) xæ iff x � Vu, xæ � Vu and Vuæ ≤ Vu On the other hand, function e can be obtained from the Walrasian demand function x by solving the system of partial differential equations

∂e(p)∂p1

= x1(p, e(p))

M ∂e(p)∂pL

= xL(p, e(p))

for any given initial conditions p°, e(p°) = w° and any given level u°. Now, by Frobenius Theorem, for L > 2 this system has a solution iff the Slutsky matrix

S(p, e(p)) = Dp x(p, e(p)) + Dw x(p, e(p))x(p, e(p))T = D p

2 e(p) is symmetric and negative semidefinite. This last condition holds whenever x satisfies (in addition to axioms (2) and (5) of Definition 8) the Weak Axiom of Revealed Preference,16 while symmetry holds only if preferences are acyclic. Hence, the whole utility-determination procedure makes sense only if it starts by attributing rationality and congruence to the agent! But, as I stress again, far from being a defect of NET, this is the mark of a non-trivial empirical theory.

4. Goudzwaard’s Objection to NET: A Reply

Goudzwaard (1980) and other Reformed authors17 have produced a number of objections against the “presuppositions” of NET. Since

16 The Weak Axiom of Revealed Preference is a particular case of the Strong

one, namely when N = 2. 17 Like Cramp (1975), Storkey (1993) and those in Tiemstra (1990). A Roman

Catholic criticism of current economic theory, together with a view of how a ‘‘Christian’’ economic theory should look like, is provided in Beed and Beed (1996).


Goudzwaard criticism is the most systematic and explicit, I shall devote this final section to analyze and respond to his objections. Goudzwaard finds in Robbins’ (and therefore also, as I have argued in Section 1, in Dooyeweerd’s) definition of economics, as the science which studies human behavior as a relationship between given ends and scarce means which have alternative uses, at least six presuppositions, namely those of: (1) scarcity, (2) individuality, (3) utility, (4) instrumentality, (5) priceability, (6) closed causality. I shall present Goudzwaard’s objections to these presuppositions, together with my reply, in the given order.

4.1. Ad Scarcity

Goudzwaard’s finds the concept of scarcity as a “subjectivistic” concept because the scarcity of means is relative to the ends pursued by the agents. He finds this leading to the following “ethically unacceptable” consequences:

(1) Scarcity is only constituted by presently living economic subjects. Thus, the methodology of NET can reckon with the provisions necessary for future generations “only to the extent that the present generation is willing to take into account the possible needs of these future generations in its own current subjective preferences.”18

(2) Subjective needs are assumed to be unlimited. This assumption seems to be a “methodological trick” to ensure unsatiability.

(3) Social costs are not taken into account in the utility functions of the agents and so they cannot be determined “at the moment.”

(4) Subjective wants are given as the expression of the autono-mous choice of economic subjects.

I find in all these objections a confusion between an explanatory and a normative use of NET and, moreover, between the assumptions of the scientist using the theory and those of the agents whose economic behavior he is trying to explain. It is just not true that NET has to tie considerations on the consumption of future generations to the utility of agents at some point in time. Consider, for instance,

18 Goudzwaard, op. cit., p. 14.


Ramsey expression for the overall utility U of any individual agent (household) in his dinamic model:

U = 0

∞

∫ u[c(t)] ⋅ ent ⋅ e-rt dt, where c(t) is the consumption of the household at time t, u[c(t)] is the utility for the agent of such consumption, ert is the family size, and ept is a measure of the consumption anxiety of present generations: r > 0 means that parents prefer a unit of their own consumption to a unit of their children’s consumption. Now, an economist may find that the parameter r is actually positive in analyzing a given economic situation. What can he do? Obviously, if he is trying to explain the behavior of the households he has to notice that fact even if he does not like it. But then the selfishness of the agent under study is not responsibility of the theory! Ramsey himself (1928) found the assumption that r > 0 as “ethically indefensible”, but then Ramsey was thinking of his model as a policy proposal. The point is that no economic theory has to be conceived as a policy proposal always or even mainly. Nonsatiability is not a necessary assumption of NET, but only of some of its specializations. It is made in many occasions to simplify the proof of the existence of competitive equilibria, but it can actually be weakened to the assumption of local nonsatiability.19 Local nonsatiability does not require that subjective needs be un-limited, since it can be satisfied in (the interior of) a compact set of consumption menus. At any rate, by definition of “economic situation”, if there is no scarcity, there is no economic problem either. Scarcity is what makes a situation be economic in Dooye-weerd’s sense. Regarding objections (3) and (4), it is true that the usual com-petitive equilibria models of NET are built under the assumption that the utilities of the agents do not depend upon those of the other agents, but that does not preclude having utility functions depending on the actions of other agents. For an example of a model with these characteristics, see McKenzie (1955). The problem with these models is that proofs and computations become far more complicated.

19 We say that a preference relation over a set A is locally nonsatiated iff or any

vector x � A there are more preferred vectors arbitrarily close to x.


4.2. Ad Individuality and Utility

Goudzwaard raises the important methodological question for NET of how utility is determined by the working economist: “How does the economist know people’s preferences, their “ends”? In what way or through what mechanism do these ends become accesible to theoretical economic analysis? After dismissing the “theory of revealed preference” as leading to inconsistencies or the trivial tautology that “the consumer always acts as he acts”,20 he claims that the question is answered

either by referring to what consumers and other economic subjects concretely do in the market, leaving the economist with almost nothing to explain; or by referring to presupposed individual order-ing schemes in which the urgency of the desire for a good is measured according to its capacity to give utility. Accordingly, the preferences “revealed” in the market are viewed as the result of the weighing-process, by so many individuals, of these preordered utilities.21

If I understand Goudzwaard well, he means to say that NET is forced into the assumption of individuality, namely, the claim that collective needs [the needs of corporations] do not originate at the level of the corporate entity, but must be derived in their root from existing individual needs, because it cannot determine the utility of corporate entities due to two reasons: (i) revealed preference is cir-cular and leads nowhere; (ii) utility is a psychological magnitude that can be experienced only by a living individual and, as Arrow’s Impossibility Theorem shows, individual utilities cannot be aggregated. It is not at all clear whether Goudzwaard is atttributing to NET the claim that utility can be determined only for individuals through some process of psychological analysis, but in fact NET’s methodology for determining utility (as shown above) does not have to assume that the agent is an individual and, moreover, utility is not a psychological magnitude for NET. In fact, the literature usually refers to the consumers as “households”, to the producers as “firms”,22 and really does not care whether the consumption or production decisions are taken by some individual or an administration board. The utilities do not have to represent preferences or desires of some individual but may reflect those of a corporate entity. Utility was seen

20 See p. 9. 21 See p. 10. 22 See, for instance, Debreu (1959), p. 50.


during the xix century as a psychological magnitude (for instance, by Bentham) but that view is no longer held. Thus, the “presupposition” of individuality is just non-existent. Utility is not a psychological magnitude (although in some models it can be interpreted as such) but—as I have tried to show above—precisely a NET-theoretic term and so irreducible to any psychological theory. NET has its own ways of measuring utility and these ways possess that circularity which is typical of theoretical terms in any interesting empirical theory, like mechanics. The circularity is not tautological because the utility functions thus determined can be transported into another model (by means of constraints) and yield valuable information about economic behavior in those other models. Finally, NET is not commited to utilitarianism or any other ethical view: of course it ignores all distinctions between good and evil, since it is not an ethical theory. The only norm that it deems as relevant from its own viewpoint is the norm of efficiency, but this norm is not moral or justitial: it is rather the central norm of the economic modality. NET does not transform the totality of human motives, norms and values into the status of “individual feelings” of utility and disutility, “a grey mass without any qualitative distinction”. It has to do only with the problem of making efficient use of resources given certain ends, and that presupposes a preference ordering by the agent (see Section 1). NET does not deny that

Human activity is far too complex to be understood simply by the concept of rationality in the ordering of (dis)utilities [...] the formation of human needs and the development of patterns of economic behavior take place in reaction to or as an (appropriate or inappropriate) answer to creational norms for the totality of life.23

That is right: only that NET does not pretend to understand the whole of human activity, or that all human activities are guided by the economic norm. As in any empirical theory, the domain of intended applications of NET (I) is restricted, and the question whether this or that behavior belongs to I is an entirely empirical matter. Roughly, the claim is that only those systems of actions whose guiding function is economic are to be found in I.

23 See p. 17.


4.3. Ad Instrumentality

Goudzwaard attributes to NET the claim that there is a clear-cut, fixed distinction among two categories of goods, namely those that are merely means used in production, and those that are only ends, exclusively used in consumption. He also believes that this distinction makes of NET “a servant of an economic system which has growing production as its real and ultimate economic focus”.24 Against this, he admonishes that

(1) We must recognize that in the choice of the means as well as in the choice of the ends, non-economic considerations play a role along with economic considerations.

(2) We must recognize that there can be a constant interplay or trading off between means and ends, such that what in one instance can be perceived as an end may, in another context, be a means. There are not two pre-ordered, mutually exclusive categories of “means” and “ends”.25

I do not see how NET could collide with the first of these admo-nishions. NET is not precluding the application of any type of norms both to determining the ends and the means. Many considerations can be made to establish, e.g. the set of production possibilities or acceptable consumption menus. NET’s machinery starts to work once these sets have been determined, whether they are “morally” or “non-morally” determined. NET is not a normative theory about what is acceptable as a means or an end. As an explanatory theory it can be used, e.g. to determine whether the use of the means by the SS was efficient given two simultaneous ends: (i) exterminating the Jewish people and (ii) defeating Stalin in Russia. What NET can say in this regard is whether Hitler was (or was not) efficient in the use of the means for such ends. It has nothing (and need not have something) to say on the moral quality of these means and ends. Admonishion (2) is just misplaced if it implies a denial of the (classical) distinction between the sphere of production and that of consumption. It is clearly not the same a commodity that can be used only in a production process than one that can be used only in direct consumption by a household. And some goods can be used both in

24 See p. 21. 25 Goudzwaard, op. cit., p. 20.


production and in consumption (like a car). Yet, it is correct if interpreted as meaning that in some model of the theory, or in the same model for two agents, the same type of commodity can be a means and an end. Moreover, this must be so in general equilibrium with production, where one firm produces a means that another firm needs to produce another end. For the first firm, producing the means is an end; for the second, this means is precisely that: a means through which it achieves its own end. This is the meaning of Sraffa’s famous phrase “production of commodities by means of commo-dities” which Goudzwaard himself adopts,26 I suppose, as an example of good economic theorizing. But the production of commodities by means of commodities in Goudzwaard example, taken from Sraffa (1960), is just a specific and fairly simple model of NET (when the production possibility sets are assumed to be convex polyhedral cones, there is no joint production and no alternative techniques), as my book (I hope) makes it clear.27

4.4. Ad Priceability

Goudzwaard finds the “presuppositions” of scarcity and priceability closely linked. “There can be no scarcity without priceability” would be the link. This is taken to mean that NET cannot make an economic valuation of useful goods except through pricing: a resource is deemed as scarce by NET iff it has a positive price. Yet, some valuable things like the ozone in the biosphere are becoming scarce (not in Mexico City, but where it is needed, up there in the sky!) but there is hardly a way of pricing such a “good”. This is how NET has contributed—in Goudzwaard’s view—to the “general Western opinion that something without a price can be perceived and treated as something without intrinsic economic value”.28 It is not clear, first of all, what Goudzwaard means by “intrinsic economic value”. By his example (the biosphere), I suppose he means by it any thing that can be used by man or eventually depleted. In that sense, the iron deposits in Mars (if there is any) have an intrinsic economic value. Now, NET does not deny that they can be used or entirely depleted. The point is that NET is a theory about decision-taking by human individuals or social organizations. In the

26 On p. 36. 27 See García de la Sienra (1992). 28 See p. 22.


case of Mars it is perhaps too soon (although not impossible) to study the possible decisions regarding its iron deposits. In the case of the biosphere those studies can and should be made, and surely they would show that there are costs attached to maintaining a biosphere with certain qualities. But it is really a confusion to blame NET for the stupidity of the human race (or of the powerful firms or governments not willing to do anything).

4.5. Ad Closed Causality

Goudzwaard’s attribution to NET of a Kantian theory of causality follows the same pattern of previous unwarranted attributions. Again, the fact that some avowed normal scientists within NET raise a Kantian interpretation of this theory does not mean that there is anything in its axioms committing whoever adopts them for purposes of economic analysis to such an interpretation. The assumption of causal closedness is a heuristic supposition adopted provisionally only for purposes of the analysis at hand. It is similar to the assumption made in classical mechanics, for instance, when the resistance of the air for bodies in free fall is negligible. Naturally, the very nature of the problem may indicate that such an assumption is wrong, that other factors must be taken into account. And such factors may be so complicated that actually preclude the possibility of building a model of NET that explains the observed behavior. When that happens, the case may be that the situation that is being modeled is not guided by the economic norm, but is a situation that finds its guiding function in another sphere. At any rate, how good an approximation is a model of NET that neglects certain factors is an empirical question that must tackled by means of the methods proper to the theory. To neglect the environment of a phenomenon conceptualized in a certain way does not mean to neglect the existence of such an environment, as the Kantian interpretation seems to suggest.29

29 Indeed, some of the main defenders of the SM held the Kantian view in the

main exposition of the metatheory (Balzer, Moulines and Sneed (1987)). For my criticism of the Kantian interpretation of SM, see García de la Sienra (1988). This is not the place to address this topic, but it must be clear to the reader that my adoption of the metatheoretic apparatus of SM ---or my willingness to defend NET as an economic theory--- in no way make me feel commited to Kantian epistemology.


5. Conclusions

Goudzwaard’s account of NET is not correct. He confuses NET with the philosophical view of some of its adherents and attributes to the theory claims which the theory does not make and cannot make. On the other hand, he wants an economic theory to do the job proper to a social philosophy. An integrated view of human action cannot be provided by economics, but only by philosophy. NET fulfills fairly well its task of providing a framework to study the economic aspect of human behavior, from the viewpoint of the fundamental modal law of economics. This is the law of utility maximization (see Definition 7), which rules human behavior when this behavior is guided by the norm of efficiency. NET does not claim that all aspects of human behavior can be seen as cases of utility-maximization behavior.

References

Balzer, W., C.U. Moulines and J.D. Sneed. An Architectonic for Science. The Structuralist Program. Dordrecht: Reidel, 1987.

Balzer, W. and C. U. Moulines. “Die Grundstruktur der klassischen Partikelmechanik und ihre Spezialisierungen”. In: Zeitschrift für Naturforschung 36(a) (1981).

— Eds. Structuralist Knowledge Representations: Paradigmatic Examples. Amsterdam: Rodopi, (forthcoming).

Beed, C. and C. Beed. “A Christian Perspective on Economics”. In The Journal of Economic Methodology 3(1) (1996), 91-112.

Bourbaki, N. Theory of Sets. Boston/Reading: Herman & Addi-son-Wesley, 1968.

Cramp, A. B. Notes Toward a Christian Critique of Secular Economic Theory. Toronto: Institute for Christian Studies, 1975.

Debreu, G. Theory of Value. New Haven: Yale University Press, 1959. Dooyeweerd, H. De wijsbegeerte der wetsidee. Amsterdam: H. J. Paris,

1935-6. — A New Critique of Theoretical Thought (4 vols.). Jordan Station:

Paideia, 1984. García de la Sienra, A. Review of Balzer, Moulines and Sneed (1987).

In Theoria (Lund) 54 (1988), 73-78. — The Logical Foundations of the Marxian Theory of Value. Dordrecht:

Kluwer, 1992.


— “The Theory of Finite Games in Extensive Form”. In: C.U. Moulines and W. Balzer, Structuralist Knowledge Representations: Paradigmatic Examples.

Goudzwaard, B. Toward Reformation in Economics. Toronto: Institute for Christian Studies, 1980.

Houthakker, H. S. “Revealed Preference and the Utility Function”. In Economica 17 (1950), 159-174.

Mas-Collel, A., M.D. Whinston and J.R. Green. Microeconomic Theory. New York/Oxford: Oxford University Press, 1995.

McKenzie, L.W., “Competitive Equilibrium with Dependent Con-sumer Preferences”. In: H.A. Antosiewicz (ed.), Proceedings of the Second Symposium in Linear Programming. Washington: Washington National Bureau of Standards, 1955, 277-294.

Ramsey, F.P., “A Mathematical Theory of Saving”. In Economic Journal 38 (1928), 543-559.

Richter, M.K. “Revealed Preference Theory”. In Econometrica 34(3) (1966), 635-645.

Robbins, L., An Essay on the Nature and Significance of Economic Science. New York: New York University Press, 1984.

Sraffa, P. Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press, 1960.

Storkey, A. Foundational Epistemologies in Consumption Theory. Amsterdam: Vrije Universiteit University Press, 1993.

Tiemstra, J.P. (ed.). Reforming Economics. Lewinston/Queenston/ Lampeter: The Edwin Mellen Press, 1990.

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Garcia de la Sienra The Modal Laws of Economics