Preference ordering under a pigovian emulative system

Preference Ordering Under a Pigovian Emulative System

HIROAKI HAYAKAWA*

More than two decades ago Kenneth Arrow sharpened the theory o f social choice by distin- guishing between individual tastes and values [2, p. 18]. In principle, he pointed out that the preference ordering by values of the individual, being inclusive o f all his desires, is primarily relevant for social choice and for the achievement o f a social maximum. Along with Arrow, and in an invidious system, it may also be argued that the preference ordering based on social values of emulat ion is primarily determinate for the choice and the satisfaction of the individual.

The effects of social values of emulation, or, more generally, effects of interdependence or externalities, on the preference ordering and on

the demand of an individual have been well ex- plored in the literature [18, 14, 8, 13, 5~ 10, 17, 11,9 , 3, 6, 7]. Previously, however, such effects have been treated almost always as giving rise to a nonfunctional component o f demand. What has not been treated in greater depth is the question: what happens if social values of emulat ion completely dominate the preference ordering of the individual? The objective of this paper is four-fold. First, we shall give a more precise meaning to social values of emulation, and thus identify reference-group-taking as the mechanism by which distinction is sought (Section I). Second, we present a static model of the preference ordering according to social values of emulat ion (Section II). Third, we introduce a particular way of looking at dynamic changes of an individual 's preferences in the context of the emulative system (Section III). Fourth , we discuss some implications of this model upon the theory of consumer choice and on welfare economics (Section IV).

*University of Georgia. The author wishes to ex- press appreciation to P. H. Ray, University of Michigan; L. D. Taylor, University of Axizona; O. O. Allsbrook,

17

I. Social Values of Emulation

In an invidious system, or one in which the structure of differentiated social, roles and posi- tions is integrated around a system of pecuniary rewards and social prestige wi th 'a well defined social status scale, individuals are motivated to gain reputation, social prestige, higher status identification, etc. Here such motivation will be the most persistent and so the strongest among all motives in conventional economic decisions. This motivation is expressed via the mechanism of reference-group-taking. That is, individuals seek to climb the social status ladder by choos- ing particular reference groups for emulation, or avoidance. A. C. Pigou once elucidated the

nature o f this mechanism when he wrote [15, p. 23] :

"In fact, however, distinction is usually to be found, not in being in the swim in general, nor yet in being out of the swin in general, but in a combination of resemblance to certain persons and of difference from certain other persons. If the consumption of a commodity increases among those classes with whom I wish to be associated, my demand for it increases, but, if the consumption increases among those from whom I wish to separate myself, it decreases. Suppose, for example, that I am the mayor of a provincial town. In that case, if the Victorian Order becomes a more ordinary decoration for marquises, my desire for the decoration will be enhanced, but, if it becomes a more ordinary decoration for crossingsweepers, I shall be tempted to regard its presentation to myself as an insult. Further- more, both among the persons whom a man wishes to resemble, and among those from whom he wishes to separate himself, some are usually much more important to him than others.'"

A. C. Pigou's idea of this mechanism can be interpreted accordingly. As a function of one's standing in a social status ladder, an individual orients his behavior to a set o f reference groups

A. L. Danielsen, and C. D. DeLorme, University of Georgia; and Gordon Tullock, Virginia Polytechnic In- stitute and State University, for their helpful comments.

18 ATLANTIC ECONOMIC JOURNAL

in his efforts to gain higher status identification and to avoid lower status identification. Some reference groups have positive (i.e., emulation) effects, and others have negative (i.e., avoidance) effects on one's consumption behavior. Among those groups one wishes to emulate as well as among those groups one wishes to avoid, both positive and negative effects differ in strength. Furthermore, the individual's reference groups can be ordered in terms of their social status. Al- though an individual has a number of reference groups for emulation and avoidance, he can emulate the life style of only one such group. This is because he must achieve the complementarity among wants and goods required for a successful emulation of the life style.

Suppose, from the Pigovian example, that a politician in a provincial town takes a group known as "marquises" as his reference group. In order to gain distinction, he necessarily seeks to acquire wants for that which is typical and popular among "marquises." He acts as a copy- cat toward that class. I f he is given something which is popular among lower status groups, he takes such presentation as an insult, since it gives him lower status identification. He thus acts as a snob to lower status groups. On the other hand, if he is given something which is typical among higher status groups than "marquises," he will be embarrassed again in the sense either that it does not go along well with the accepted life style of "marquises" (which requires a certain complementarity among goods), or that it is ob- jectionable through negative sanctions for deviation from the accepted life style of "marquises." Moreover, the politician takes the class of "marquises" as his reference group only if it is socially acceptable to do so. That is, his reference-group- taking is not based on his personal tastes but is a function of his and other social groups' standing in the social status scale.

There are four principles inherent in reference-group-taking behavior. Firstly, an individual has psychological motivation to emulate other social status groups in proportion to the rewards of upward status identification or to

avoid them in proportion to the threat of lower status identification. The higher the social status of an emulated group, the greater is the psychological satisfaction (due to a gain in status). This is a psychological principle, which is an encour- aging factor for emulation of higher status groups. Secondly, although the individual may want to gain in social status, there are positive sanctions for conformity and negative sanctions for deviation. I f one seeks to emulate a much higher status group, he can do so only at the ex- pense of increasing group pressure against deviation. This is a sociological principle, which discourages emulation (conforming to group norms is good, and deviation from them is bad). Third- ly, even if one wants to emulate a particular group, efforts at emulation will not be successful if there is insufficient factual information about life style activities of the group available to him. The degree of difficulty in obtaining such information about a life style is related to social distance between the status of an individual and that of an emulated group. This is a com- munication principle, which works against emulation of distant social groups. Finally, an emu- lating individual has to keep in mind that different social groups have different life styles, and that associated consumption patterns are different. The difference between consumption patterns of two social groups is expected to widen as a function of social distance between them. This means that if one wants to emulate the life style of a higher social status group, he will have to bear the cost of losing the complementarity among goods required of his present life style. Furthermore, information gathering and pro- cessing is time-consuming and costly. This is an economic principle, which again discourages emulation. It is apparent, then, that a particular reference group which an individual can and does adopt for successful emulation is a result of these four principles [16, pp. 281-295].

In abstracting the Pigovian idea of emulation via the scheme of reference-group-taking, I shall assume that social groups have well specified clusters of wants which are defined as comple-

HAYAKAWA:

mentary because of the interconnections that are established by virtue of life style activities. Clearly, the preferences of an individual in an invidious system are profoundly influenced by his standards of emulation and by those standards socially accepted. In particular, these preferences are determined by complementary wants of a particular reference group chosen as a result of our four principles. A vital question under this approach is the impression on an individual's preference map when he accepts complementary wants of his chosen reference group by copying the accepted consumption pattern and life style activities. This is a question which deserves some attention in at least a more formal way. The following section addresses this question.

II. A Model of Individual Preferences

The objective here is to analyze effects of socially acquired wants upon the structure of preferences of an individual. The foregoing discus- sion of a Pigovian emulative system can be con- densed into the following two axioms.

Axiom 1: Social groups exist. They are characterized by distinct life styles which project clusters of complementary wants, and by associated efficient consumption technologies.

Axiom 2: The individual, as a function of his and other groups' social status, takes a social group as his reference group and emulates its life style in his effort to climb the social status ladder.

First, we abstract pertinent aspects of the single reference-group-taking characterized by Axiom 1 and 2, and state them as assumptions to be satisfied by consumer preferences. Note that in line with Lancaster [12], the consumption set in this analysis is taken to be the characteristics space rather than the goods space.

There are norms in what members of any social group consume. Although such norms are objectively present, a member's perception of them may not be the same as that of another. For our analysis, it is the fact that such perception exists which matters. Thus, the life style of a social group can be given by a composition of

PREFERENCE ORDERING 19

characteristics representing such perceived norms. This is explicit in the first assumption.

Assumption 1: In the consumption set of the individual, there is a single most desired bundle of characteristics (to be called the optimum consumption bundle and to be denoted by X* hereafter) which represents his perception of norms of what members of his social reference group consume. It is assumed to be an interior point of the consumption set.

Such a bundle of characteristics is the most desired in the sense that the individual perceives it to be the most socially acceptable and popular among members of his social reference group. Due to social pressure of negative sanctions for deviation and positive sanctions for conformity, any deviation from this optimum consumption bundle is expected to leave the consumer worse off. The greater is this deviation, the worse off the consumer becomes due to a decline in social acceptability. Therefore,

Assumption 2: Any deviation from the optimum consumption bundle necessarily makes the individual worse off due to a decline in social acceptability. Moreover, the further he deviates from the optimum consumption bundle, the worse off he becomes. For example, in Figure I, a bundle X 2 is more deviant from X* than another bundle X 1 ; therefore, X 2 is less preferred to X 1 . (See Figure I.)

Figure I

X ~e

x 2

o The next assumption is closely related to As-

sumption 1. Let us assume that, if the individual is made worse off in shifting his consumption from one bundle X 1 to another X 2, then there is only a decline in his welfare in the direction of the shift beyond the less preferred bundle X 2 . In point of fact, this assumption is equivalent to the assumption of convexity normally as-


sumed in classical theory whereby the preference relation satisfied continuity.

Assumption 3." (Directionality) Given two bundles of characteristics, X 1 and X 2, if X ~ is preferred to X 2, then any bundle X on an ex- tended line segment through X 2 is less preferred to X 1 . (See Figure II.)

F i g u r e Tr

X 2

X

Since social acceptability does not decline discontinuously as deviation from the optimum consumption bundle increases, we also assume that the individual's preferences based on such acceptability satisfy continuity.

Assumption 4: (Continuity) The consumer's preference relation based on social acceptability satisfies continuity.

Slice the space of characteristics by a two di- mensional linear space, and denote this slice by P. A ray coming from the origin and passing through the optimum consumption bundle X* divides this slice into two parts, P1 and Pz. This ray is denoted by R*. Choose an arbitrary bundle X ° on R*, and draw a perpendicular line through it. Denote this line by L(X°). That part ofL(X °) which lies in P1 (or Pz) is then denoted by LI(X °) (or L2(X°)). (See Figure III.)Note

that any bundle of characteristics along the ray R * has the same complementarity among characteristics as the optimum consumption bundle (hereafter called the ray of optimum complementarity). Therefore, a direct deviation from such a ray, such as from X ° to X 1 on P, in Fig- ure III, should only decrease the individual's welfare because of loss of optimum complementarity. This raises another assumption.

Assumption 5: Along the ray of optimum complementarity R*, any direct deviation, such as from )t o to X 1 , in Figure III, makes the individual worse off due to loss of optimum complementarity.

We assume finally that the individual is ration- al in the sense that his preference relation based on social acceptability satisfies transitivity.

Assumption 6: The preference relation is transitive.

Given Assumptions, 1, 2, 3, 4, 5, and 6, a preference map of the individual can be determined. Choose a bundle X ° on R*, and suppose that X ° lies between the origin and X*. Take an arbitrary bundle Y in region R I (Figure IV). By Assumption 5, Y is less preferred to yO, and by Assumption 2, ]to is less preferred to X °. Hence, Y is less preferred to X ° by transitivity. Like- wise, we can show that any bundle in region R II (Figure IV) is less preferred to X °. Thus, an indifference curve through X ° lies neither in R I nor in R II. Similarly, if X ° is further away from the origin than X*, an indifference curve through X ° lies neither in R I ' nor in R II' (Figure IV).

Figure Trr

X o )

0

Figure r~

Xl ~ 1 - R* \ RI \ ~LI(X)~""~ X°

0

HAYAKAWA: PREFERENCE ORDERING 21

Knowing this, we may show that on P, for any bundle X ° on R*, L I(X) (where X is another bundle on R* between )t o and X*) has a unique bundle of characteristics X ' which is equally preferred to )t °, provided X is sufficiently close to X ° (See Figure IV). To show this, choose a bundle X 1 different from X ° on LI(X°). Under Assumption 5, X 1 is less preferred to X °. By continuity there is a neighborhood N(X 1) such that any bundle in N(X 1) is less preferred to X °. Draw a line LI(X) which intersects with N(X 1) N P, where X is between X ° and X* on R*, and then choose a bundle X 2 in the intersection. Clearly X 2 is less preferred to X °. By Assumption 2, however, Xis preferred to X °. Therefore, by continuity there must be a bundle X ' between X and X ° on L t (X) which is equally preferred to X °. Moreover, by As- sumption 5, such a bundle must be unique. Simi- larly, L2(X) (where X is between X ° and X*) has a unique bundle which is equally preferred to X °, provided that X is in a neighborhood of X °. Thus, by shifting L(X) toward X* we can trace an indifference curve through X °. By the directionality and the continuity assumptions, such a curve is, in a neighborhood of X °, convex when X ° lies between the origin and X* and concave when X ° is further away from the origin than X*. (See Figure V).

F i g u r e ~ Z

R ~

O

Furthermore, since the preference relation is continuous and because any deviation from the optimum consumption bundle X* makes the individual worse off, indifference curves in a neighborhood of X* must be nested around X* as in Figure V.

III. Dynamic Changes of Consumer Preferences

According to the static model of the previous section, an individual follows consumption patterns of a social reference group. And, in an invidious system, such reference-group-taking is a function of where one is located in the social status ladder. To the extent that real income is probably the most effective measure in deter- mining one's social status, sufficiently large changes in this variable are likely to change an individual's social status. Therefore, his social reference group would change as well. A new reference group would offer different consumption patterns and technologies, and as they are acquired, the individual's preference system un- dergoes dynamic changes. The process of dynamic change can be understood in our model in the following way.

Suppose that an individual, as a function of his present social status, takes a group G1 as his reference group. The preference map based on the group's social acceptability is drawn as M1 in Figure VI. In the same figure are shown two

Figure IZ[

CHARACTERISTIC X I

R?

I .M 2 R~

" R;

0 CHARACTERISTIC X z

more preference maps that the individual would have acquired had he associated with higher social status groups, G2 or G3. They are drawn as 11"I2 and M3 respectively. The consumption possibility frontier is AB, and the individual's optimum choice is X ° (under the assumption that many goods are available). As real income rises, the consumption possibility curve shifts outward from AB to a new position. The optimum choice accordingly moves up along the income-con-


sumption path C1. If the change in income is small, the individual's preference map remains the same as he associates with the same reference group; therefore, the optimum choice simply moves along the income-consumption path C~ associated with the map M~.

However, as real income rises further, consumption patterns of higher social status groups become increasingly possible, and a point may be reached when the individual abandons his earlier reference group to associate with ahigher status group. Such a point will normally be reached after realizing the optimum consumption bundle. If we assume hypothetically that this change in reference-group-taking occurs as soon as the optimum bundle is reached, and that G2 and G3 are the individual's new reference groups for higher income levels, then the income- .consumption path would be C~C2C3 with discontinuities at X~* and X~.

This type of treatment of dynamic change in preferences, particularly its simplicity, is quite appealing. Moreover, it is not without plausibil- ity, since individual preferences do appear to go through certain discrete changes as suggested here. For example, an individual's demand for unit housing, and a residential area, as well as associated goods is very much a function of his socio-economic status. As real income rises sufficiently above a previous level, one's desire for better housing and a better residential area can no longer be suppressed in an invidious system. Such a rise gives one enough claim to higher social prestige. However, once he associates with a new, socially more prestigious group and adopts a new residential area, it is unlikely that his preferences remain unchanged. In fact, rather drastic changes will be observed in his preferences as new housing and new neighborhood both require consumption of all other characteristics by the right amounts and proportions. In part this is because of individual aspiration for emulation and also because of sociai pressure for conformity to consumption patterns of a new reference group. In effect, the income rise causes a whole cluster of wants to change.

IV. Implications on Consumer Choice and Wel- fare Economics

In Section II we have given a precise charac- terization of a typical individual's preferences in a Pigovian emulative system. In such a system social values of emulation and avoidance necessi- tates choice of a particular reference group as a function of various socio-economic factors, and one's preferences are determined by norms and social acceptability of choice alternatives within a (relevant) reference group rather than by personal tastes. They are characterized by the optimum consumption bundle around which indifference curves nest; and a relevant range over which the marginal rate of substitution is positive and diminishing narrows as actual consumption approaches closer to the optimum consumption bundle. We can draw several implications for consumer theory and welfare economics from this model of individual preferences.

First, the nesting nature of the preference map repudiates the univeral applicability of the monotonicity axiom on which many welfare propositions are basedJ In fact, oncethe optimum consumption bundle is achieved, an increase in consumption of characteristics only makes the individual worse off due to a decline in social acceptability. One's objective is to at- tain stature in social prestige; hence, "more" is appreciated only to the extent that it helps the individual achieve this objective via successful reference-group-taking.

Second, since the relevant range diminishes as the optimum consumption bundle is ap- proached, the income effect of a price change becomes increasingly dominant over the substitution effect. This property implies that if a large fraction of population behave as modeled here, we can expect only poor performance of price variables in empirical demand studies. Fur- thermore, it implies growing difficulty in achier-

It is to be noted, however, that, ~though monotonicity does not hold universally in a static setting, it may hold dynamically. This is because an individual does not keep the same reference group as he moves upward in social status.

HAYAKAWA: PREFERENCE ORDERING 23

ing the stability of general equilibrium unless the efficiency substitution effect gains in domi- nance progressively as the commodity space ex- pands via product differentiation. This is so because the efficiency choice satisfies Samuelson's weak axiom of revealed preference [ 12, pp. 156- 7] .2 Interestingly enough, although product differentiation reduces the economic efficiency, here it is seen to contribute to the stability of general equilibrium.

Third, as observed in the previous section, an individual's preferences are likely to undergo rather discrete changes as he leaves an earlier reference group to associate with a higher status one. Hence, the income consumption line in the characteristics space will have kinks (if inertia is taken into account) and discontinuities. The path, when translated into the goods space through consumption technology, will also show kinks and discontinuities. Our model is consis- tent with such paths, and, therefore, with kinky and discontinuous Engel curves.

Fourth, our model implies that the income elasticity of a purchased good tends to increase as its price rises if consumption technology me- diating goods and characteristics is linear [4]. To see this, suppose that good gi is purchased at an optimal choice point A in Figure VII when

CHARACTERISTIC X I

Figure ~E]Z[

gj

• X *

C2 Ci gl

CHARACTERISTIC X 2

prices and income are given. The income-consumption path through A will look something

2 To be precise, for global stability of general equilibrium, Samuelson's weak axiom of revealed preference has to be satisfied for the entire economy.

like C1. Then let the price of good gi increase so that B becomes an optimal choice point. The income-consumption path through B becomes C2. Ceteris paribus, the income elasticity of gi at B is greater than at A, in part because the re- sponsiveness of the good to a change in real income is greater at B than a tA, also because the quantity of the good is smaller at B than at A.

Fifth, although short-run effects of a price change are likely to be insignificant, such a change may trigger a wave of dynamic emulation- avoidance movements among social groups. When a status symbol good of a particular social group becomes relatively inexpensive, there will be an emulation of its life style by members of lower status groups. A continuous encroachment will enhance an avoidance behavior on the part of the emulated, who in turn seek to move upward, and also will alter part of normal consumption patterns of the emulators themselves so that their followers have to adjust their optimum consumption bundles, and so forth. Our Pigovian emulative system clearly institutes such a long-run dynamic effect of price changes for status symbol goods.

Sixth, we have replaced the traditional assumption of utilitarian individualism with the opposite extreme that an individual accepts complementary wants of a reference group. In spite of the reversal of this basic assumption, the re- sultant individual preference map shows smooth indifference curves with the convex upper con- tour set in the characteristics space. Consequent- ly, to the extent that such preferences are mapped to the goods space without destroying the convexity property, most of the results of traditional theory still holds. This demonstrates that utilitarian individualism is sufficient but not necessary for the applicability of classical utility theory.

Seventh, what remains unchanged after reversal of the basic assumption should not obscure the significance of our model as its welfare implications are quite different. Unlike traditional theory, an individual's preferences are no longer personal as they depend on normal consumption


patterns of a reference group, which is chosen as a function of his and other social groups' status. This implies that the government can manip- ulate individual preferences to increase social welfare. For example, when changes in relative prices favor particular consumption patterns, or when pollution problems make it necessary to advocate different life styles which impose less social cost, or even when reference standards must be lowered to allow more people to achieve them (sumptuary legislation), then the government (or even private firms) could raise social welfare by popularizing or increasing the social status of reference groups which happen to prefer them. Thus, the government could interfere directly with the emulation and avoidance patterns of the society to help accomplish certain welfare objectives. Normally, individual preferences are assumed to be fixed when economic policies are made. To the extent that such emulation and avoidance patterns are well reflected in

individual preferences via reference-group-taking, the governmental intervention of this kind induces desired changes by altering individual preferences themselves. This opens a new dimen- sion to governmental role in welfare economics.

Eighth, apart from welfare implications, individual preferences are subject to manipulation via advertising campaigns. It is evident that for some products advertising strategies are directed toward associating them with certain reference groups so that emulation-avoidance patterns of the society may accelerate the diffusion process. An illusion is created, or consumers are in- formed, that consumption of particular products is part of the requirements to be regarded as successful members o f certain social groups. To promote sales this way, however, requires know- ledge of the structure of socio-economic inter- actions among various groups, of their relative popularity, and of general emulation-avoidance patterns.

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Preference ordering under a pigovian emulative system