“Endogenous Preferences”

Bachelor Thesis

Thomas Vass

Tutor: Palle Gedsoe-Kharazmi

Institute of Economics, University of Copenhagen

November 21, 2008

Abstract

In modern microeconomic theory it is often assumed that the preferences of the consumer

must be treated as “given” fundamental data and consequently that preferences are not

affected by variables that are endogenous to the economic system. This paper discusses

the consequences of relaxing this assumption. It claims that the assumption is motivated

by “the principle of ethical neutrality”, but that an overwhelming amount of everyday

anecdotal evidence suggests that endogenous preferences is an important determinant of

many economic phenomena. This encourages an attempt to incorporate these effects into

microeconomic modelling.

First a comprehensive study of the literature on the subject is carried out. In light of this,

the paper investigates how the traditional theory of consumer choice must be adapted

if prices enter the utility function. The main results is a generalized Slutsky equation

and the proposition that under such conditions demand curves for normal goods can

be upward-sloping. Comparative statics with upward-sloping demand curves are briefly

discussed, and it is concluded that with price-dependent preferences prices can react non-

continuously to continuous changes in the underlying variables. Finally, it is discussed

whether traditional welfare theoretic concepts makes any sense in evaluating economic

situations where endogenous effects are present.

Contents

1 Introduction 2

2 Exogenous preferences 3

2.1 The principle of ethical neutrality . . . . . . . . . . . . . . . . . . . . . . . 4

3 What is endogenous preferences 5

4 Past treatments 6

4.1 The foundations: Thorstein Veblen and Tibor Scitovszky . . . . . . . . . . 6

4.2 Early treatments in economics . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.3 Modern treatments in economics . . . . . . . . . . . . . . . . . . . . . . . . 8

4.3.1 Adaptive Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.3.2 Interdependent preferences . . . . . . . . . . . . . . . . . . . . . . . 8

4.3.3 Price-dependent preferences . . . . . . . . . . . . . . . . . . . . . . 10

5 Market demand with endogenous preferences 10

5.1 Setting up the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.1.1 The utility function . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.1.2 The utility maximization problem . . . . . . . . . . . . . . . . . . . 12

5.1.3 The relative price assumption . . . . . . . . . . . . . . . . . . . . . 12

5.1.4 The expenditure minimization problem . . . . . . . . . . . . . . . . 13

5.2 Invalidity of Shephard’s lemma . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2.1 Implications of the invalidity of Shephard’s Lemma . . . . . . . . . 15

5.3 The expanded Slutsky equation . . . . . . . . . . . . . . . . . . . . . . . . 15

5.4 Implications for market demand . . . . . . . . . . . . . . . . . . . . . . . . 17

5.4.1 Arrow and Hahn’s result . . . . . . . . . . . . . . . . . . . . . . . . 17

5.4.2 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6 Welfare with endogenous preferences 19

7 Conclusion 21

A Appendix 24

A.1 Proof of the expanded Slutsky equation . . . . . . . . . . . . . . . . . . . . 24

A.2 Quote from Nationaløkonomisk Tidsskrift . . . . . . . . . . . . . . . . . . . 24

1

1 Introduction

In modern microeconomic theory the preferences of the individual are often considered

as ”givens” which the economic processes must adapt to. This is not because economic

theory states that it would be impossible to dig into the psychological, sociological or

historical reasons for the utility function taking a specific form. But for many reasons,

to be discussed below, this enquiry has been seen as outside the scope of the science

of economics. This underlying principle is very clearly stated in a passage by Milton

Friedman:

Economic theory take wants as fixed. This is primarily a case of the division of

labour. The economist has little to say about the formation of wants; this is the

province of the psychologist. The economist’s task is to trace the consequences

of such wants. (Friedman, 1962 p.13)

This attitude assumes away the possibility that the utility function can be shaped by eco-

nomic pressures or even by those economic parameters which are normally said to depend

on the preferences, such as prices.

The attitude implies that in economic models the consumer arrives at a market with

endowments and certain ideas about what she would prefer in exchange for these endow-

ments (preferences). Given the endowments and preferences of the other consumers and

the available production technologies, this will give way for the determination of a price

structure that will take into account the preferences of all consumers and all feasible al-

locations and then lead to an allocation in which the demand of all agents matches what

other agents want to supply. The causality within this analysis is clear: Preferences and

production technologies determine prices, which then determine income and the outcome

of the economic exchange process.

One consequence of this is that the traditional modelling approach will a priori prevent

analysis of economic situations in which the causal direction is not so simplistic. It is

easy to imagine a situation in which a good does not have a high price because a lot of

consumers want it, but rather the consumers want the good because it has a high price.

If economic situations such as this can arise this will naturally give rise to “feedback effects”

not yet accounted for in microeconomic modelling, because the variables in the model influ-

ence the utility of individuals, which then engender new changes in the economic variables.

2

I will use the notion ”endogenous preferences” to describe a situation in which the

preferences of individuals are influenced by the distributional system itself. This termi-

nology has been introduced by Bowles (1998). Bowles reviews the extra-economic (that

is sociological, psychological, anthropological etc.) evidence for endogenous preferences

being present in real-world situations. That is not the ambition of this paper. The aim

is rather to elaborate on the consequences for economic modelling if we accept Bowles

hypothesis that preferences will in some instances be endogenous.

Note that the arguments presented here should not be understood as an attack on

economic theory as such for not taking sociological and psychological issues into account.

I am not representing the traditional critique of homo economicus as an ill-defined ana-

lytical concept for the social studies. Rather I call for an internal adjustment of economic

theory if the claim of endogenous preferences is true.

2 Exogenous preferences

In the traditional exposition preferences are treated as exogenous. Historically the main

reason for this convention is probably that Marschall dismissed the question of endogenous

preferences. After briefly touching upon the theme of relative wants in his magnum opus

“Principles of economics” he remarked that “we are exceeding the proper scope of this

book”. That meant, so to say, that it was possible to treat preferences as exogenous and

then refer to endogenous preferences as an exotic albeit interesting appendix. (Marschall,

1920). But besides this historical explanation there are good reasons why the economic

profession chose to accept this claim instead of correcting it. First of all, it is needless to say

that the assumption of exogenous preferences greatly simplifies the analytical framework

and thereby enables a parsimonious model for most economic situations. Furthermore,

the empirical knowledge of how widespread the phenomena of endogenous preferences

are, is limited, and attempts to expand this knowledge runs into conceptual difficulties in

distinguishing endogenous effects from “normal” effects 1. I claim though, that the main

reason for assuming exogenous preferences is the economical theorists’ strong aversion

against paternalism. If preferences was malleable a social planner could be tempted to

engineer peoples needs and desires. It is a prudent distance to this fact that have made

economists insist that preferences are “given”. This can be summed up as “the principle

1see for instance Pollak (1977)

3

of ethical neutrality”

2.1 The principle of ethical neutrality

The principle of ethical neutrality states that the economic theorist should not make any

value judgements about economic situations. This means, that if economic theory is to be

evaluative in any way, the commendation or condemnation of economic situations should

emanate from the economic actors.

The principle therefore entails that every individual is himself in the best position to define

what is ”the good” or the desirable for him. No one can define more ”right” preferences

with reference to some higher instance, be that a benevolent social scientist, a malevolent

dictator, theological doctrines or any other objective criterion.

One early statement of the principle can be found in Lionel Robbins famous essay ”The

Nature and Significance of Economic Science”, where he writes:

Economics is not concerned with ends as such. It assumes that human beings

have ends [...] and it asks how their progress towards their objectives is condi-

tioned by the scarcity of means. [...] The ends may be noble or they may be

base. [...] Economics takes all ends for granted. (Robbins, 1932)

This is the reason Herbert Gintis has also named the principle ”the Robbins principle”

(Gintis 1976). And the devil has many names: In yet another formulation the principle is

dubbed ”the principle of consumer sovereignty”. 2

The great strength of the principle of ethical neutrality is that we thereby avoid pater-

nalism. Which omniscient economist theorist could decide on the preferences of others?

Was the Marxian notion of ”false consciousness” not the direct cause for a lot of human

misery in the former communist dictatorships? The economic profession have therefore not

been hesitant to endorse this principle wholeheartedly. This has had a great impact on the

evolution of the profession. This impact has most of all consisted in a general observance

of the commandment to accept the individuals preferences as fundamental “given” data

for the analysis of economic systems and not to question the origin or the purposefulness

of the preferences.

The implicit assumptions in this approach has not been the subject of much debate and

2This name is ambiguous, as the concept of consumer sovereignty can sometimes also refer to an ideal

for economic systems (see for instance the works of Ludwig von Mises) and not to a demand for the

formulation of economic theory, whereas the principle of ethical neutrality can refer only to the latter.

4

has in many cases been a part of modus operandi rather than a conscious decision. One ex-

ception is Stigler and Becker (1977) who provides an articulated defence of the assumption

of fixed tastes against different “accusations” of endogenous preferences.

3 What is endogenous preferences

It is not necessary to state, that a sociological or psychological theory, which tried to

explain human needs and motivations as given, would quickly be discarded as implausible.

But this is not the question here. The question of whether economic institutions affect

individuals needs have always been a matter of banality rather than controversy. It must

be presumed that the reason these considerations has been assumed away in mainstream

economic reasoning is because of a wish to make parsimonious and elegant models - not

as a claim to realism.

The traditional taboo, described in the previous section, not to question the origin of pref-

erence orderings has carried many fruits, but is also prohibitive when carrying out analysis

of many important economic phenomena. In recent years it has become the standard ap-

proach in most microeconomic models to explicitly model the strategic interdependencies

between agents, but this has not yet spread to the theory of choice behaviour.

On this background it would be obvious to try to extend the theory of choice by taking

into account, that the agents’ relative position in the economy determines their wants and

desires. In its extreme form this could be said to be the ”vulgar Marxist” position that the

nature of the economy and the position of an individual within the economy completely

determine the ideas and behaviour of the individual - compromising wants, desires and

preferences. But there is no need to defend such a strong thesis. Consider the range of

economic phenomena from everyday anecdotal experiences of economic life, that suggest

preferences are affected by the consumer’s place in the economy: The phenomenon of ex-

clusivity - owning something that no one else can afford, the phenomenon of “keeping up

with the Joneses”, the phenomenon of simulating one’s peers, conformity etc. etc. The

list goes on. This suggests that it would be a relevant task to consider how endogenous

preferences could be incorporated into microeconomic modelling.

5

4 Past treatments

4.1 The foundations: Thorstein Veblen and Tibor Scitovszky

Thorstein Veblen When it comes to discussing the relevance of endogenous prefer-

ences within the history of economic thought one figure stands out: Norwegian-American

economist Thorstein Veblen. Veblen was a key figure of the Institutionalist School, which

dominated American economics for a brief period in the end of the nineteenth century. It

is not that Veblen was the first to touch upon the subject. John Rae, writing before 1930,

had already given a treatment of the problem along Veblenian lines (Rae, 1905), and there

is allusions to the concept already in the works of the roman poet Horace (Leibenstein,

1950), but Veblen was the first to treat it ekstensively.

In “The Theory of the Leisure Class” (1899) Veblen laid forth the thesis that the motiva-

tions for consumption choices are always socially acquired. The drive behind consumption

is not the satisfaction of intrinsic wants but rather the achievement of social status. This

opens up for what Veblen labels “Conspicuous Consumption”

Since the consumption of these more excellent goods is an evidence of wealth,

it becomes honorific; and conversely, the failure to consume in due quantity

and quality becomes a mark of inferiority and demerit. [...] Conspicuous

consumption of valuable goods is a means of reputability to the gentleman of

leisure. As wealth accumulates on his hands, his own unaided effort will not

avail to sufficiently put his opulence in evidence. (Veblen 1899 p.75)

Veblen analyses in depth the sociological and psychological motives which lead to the

concept of conspicuous consumption as the prime vehicle of social esteem, but I will not

go into the details of this derivation or its validity. It will suffice here to note that this

work is one of the most significant evocations of endogenous preferences in the history of

economic thought.

Scitovszky Tibor Scitovszky in a famous essay underlines the widespread effect that

price has as an index of quality. He notes that “economists are wont to minimize the

importance of this factor, fearing the havoc it may wreak with the whole theory of choice”

(Scitovszky 1945). He claims that it is not irrational for a layman consumer to judge the

quality of products by their prices if he expects other consumers to be experts. If the

demand of the other consumers actually is determined by the quality then the interplay

of supply and demand will determine a price that can be trusted. The phenomenon of

6

endogenous preferences can arise in a market with frequent introduction of new products

where most consumers are laymen. If the average consumer judges quality by price (and

this can be the only way to judge quality) this can tempt suppliers to use the price tag

to influence the perception of quality. This would create choice behaviour where price

influences demand positively. 3

4.2 Early treatments in economics

Even though the subject matter is economical in the sense that it is about consumer choice,

Veblen’s and Scitovszky’s treatments are in the more sociological end of the spectre (at

least if we use the contemporary scientific division of labour as yardstick) and they do not

attempt to aid their reasoning with economic modelling.

Inside the field of mainstream economics the first one to notice the problem was Pigou

in connection with his work on external economies (Pigou 1929). The first instances of

formal modelling of the ideas date back to at least James Duesenburry’s ”Relative income

hypothesis” (Duesenberry 1949), which will be discussed later. The most influential and

oft-quoted paper from this period is Harry S. Leibenstein’s paper entitled ”Bandwagon,

snob and Veblen effects in the theory of consumer’s demand” (Leibenstein 1950).

Leibenstein poses the question as a problem of aggregating demand functions, pointing out

that the assumption of individual demand curves as being independent of other demand

curves is unrealistic. He recognises three external effects on the utility of the individual,

which he defines to be

The bandwagon effect, which is said to exist whenever the demand for a commodity

is increased due to the fact that others are consuming the same good.

The snob effect, which is said to exist whenever the demand for a commodity is de-

creased due to the fact that others are consuming the same good.

The Veblen effect, which is said to exist whenever the demand for a commodity is

increased due to the fact that it has a high price.

Leibensteins article furthermore proceeds with a graphical analysis of these effects. He

concludes that ’non-additivity is not necessarily an insurmountable obstacle‘ in the sense

that well-defined market demand curves can be achieved.

3Actually the process described by Scitovszky can be said to function even subconsciously. In a recent

study by XXXX it is shown that consumers judgement of the quality of wine is dependent on the price

tag (REFERENCE)

7

4.3 Modern treatments in economics

Subsequent treatments of endogenous preferences in the literature can be divided into cat-

egories that more or less coincide with Leibenstein’s 3 effects. These 3 different strands in

the literature I call i) habit formation/adaptive preferences, ii) interdependent preferences

and iii) price-dependent preferences, thereby drawing on the terminology of Pollak, who

is the only theorist who have submitted work within all three strands.

4.3.1 Adaptive Preferences

Adaptive preferences is in effect when agents are forming habits, in the sense that future

preferences depend on past consumption. Most of the literature on endogenous preferences

concentrates on habit formation as a source of endogenous preferences. This literature

begins with C.C. von Weizsacker’s “Notes on endogenous change of tastes” (von Weizsacker

1971) and is followed by Pollak (1970). Throughout this strand a discussion of whether

habit formation should be considered myopic or rational occurs: That is, if we acknowledge

that past consumption affects current preferences, is this happening “behind the back”

of the economic agents or should we leave open the possibility of “rational preference

moldering”? Even though von Weizsacker acknowledges the possibility of the latter 4 he

and Pollak both consider myopic preference changes. Later on Spinnewijn took up von

Weizsackers challenge in footnote 4 and described rational habit formation (Spinnewijn

1981). The issue has been studied econometrically by Pashardes, who finds that myopic

preference formation are rejected by his data, whereas rational preference moldering is not

(Pashardes 1986). 5.

4.3.2 Interdependent preferences

Interdependent preferences corresponds to the case when utility depends not only on ab-

solute consumption, but also the consumption of other agents. In a classic approach

utility depends on the relative consumption to the average consumption within a group

(the ”Joneses”). This is the approach used by Duesenburry (1949) (see below) and Pollak

(1976).

Another approach, which has proven more fruitfull, builds upon Hirsch’s definition of a

4 “It will require another paper to discuss this problem of intertemporal decision making in view of

anticipated or planned changes of tastes.”5Another not very remarked book is Robin Hahnel and Michael Alberts “Quiet revolution in Welfare

Theory” (1990), which uses rational habit formation to substantiate a full-scale critique of “the paradigm

of welfare theory”

8

positional good (Hirsch 1976). The consumers utility from certain goods is not derived

from the amount consumed, but from the ordinal rank in an ordering of all consumers

by the amount of the good consumed. This is the approach used by Frank (1985) and

more recently by Hopkins and Kornienko (2004). Hopkins and Kornienko provide a so-

phisticated model in a game-theoretic context of status-seeking in a world where status

depends on relative consumption. They show that as society becomes richer people spend

a greater proportion of their income on conspicuous consumption, and that utility at a

given level of income declines. This is also the result in Curtis and Eswaran (2008), who

shows that as productivity increases, goods that are valued for their relative consumption

will eventually crowd out all other economic activity. These results are in line with the

predictions of Veblen 6

Does endogenous preferences explain “the consumption puzzle”? For many

years the economics profession was puzzled by the fact that the average propensity to con-

sume falls with income in cross-sectional data, but is constant in time-series data. This

is a problem for a standard Keynesian consumption function. It was first discovered by

Kuznet and has been known as the Kuznet puzzle. The traditional way of approaching

the problem is to replace the Keynesian consumption function with Miltons Friedman’s

“Permanent Income Hypothesis” or Modigliani’s “Life Cycle Hypothesis”. These theories

insist that cross-sectional income differences can be explained by life-cycle differences and

transitory income - high income individuals are saving more in order to maintain con-

sumption levels in periods with lower income. A major drawback for these theories is,

that econometric attempts to eliminate the effect of transitory earnings on consumption

does not show that low-income and high-income individuals save the same fraction (Frank

1985).

Duesenberry had already in 1949 suggested an alternative explanation known as the “Rel-

ative Income Hypothesis” (Duesenberry 1949) solving this problem by claiming consump-

tion to be a positional good. That would explain why income has a positive effect on av-

erage propensity to consume in cross-sectional data (where average consumption is fixed),

but not in time-series data (where average income is rising over time). Duesenburry’s the-

6“it is necessary in order to his own peace of mind that an individual should possess as large a portion of

goods as others with whom he is accustomed to class himself; and it is extremely gratifying to possess more

than others. But as fast as a person makes new acquisitions, and becomes accustomed to the resulting

new standard of wealth, the new standard forthwith ceases to afford appreciably greater satisfaction than

the old standard did. [...] The normal individual will live in chronic dissatisfaction with his present lot”

(Veblen 1899)

9

sis was abandoned (prematurely) by the economic profession, probably due to the forth-

coming of Friedmans explanation, which was grounded in utility-maximizing behaviour,

instead of sociological notions, and therefore perceived superior. Appendix A.2 contains

a quote from the Danish journal ”Nationaløkonomisk Tidsskrift” review of Duesenberrys

book from 1951.

4.3.3 Price-dependent preferences

Price-dependent preferences is finally the case where consumer utility depends directly on

the price vector. Arrow and Kahn are the first to include the price vector in the utility

function (Arrow and Kahn, 1971), in a brief passage of “General competitive analysis”.

The two main articles on the subject is Pollak’s “Price-dependent preferences” (Pollak

1975) and Kalman’s “Theory of consumer demand when price enter the utility function”

(Kalman 1969). Pollak and Arrow & Kahn use what Pollak defines to be the conditional

approach (Pollak 1975), whereas Kalman uses an unconditional approach. In the condi-

tional approach the preference relation itself is conditional on the price vector, such that

for instance “XA is preferred to XB for price vector p” can be written as XA �p XB. In

the unconditional approach preferences are defined over pairs of goods and prices, so that

for instance “XA under price vector PA is preferred to XB under price vector PB” can be

written as (XA, PA) � (XB, PB).

Lastly, there have been attempts to model Veblen’s theory of conspicuous consump-

tion as a signalling game with prices as strategic variables. This approach is actually

very much in line with the ideas of Veblen. In Bagwell and Bernheim (1996) consumers

can choose between different brands of identical goods. A representative social agent can

observe the brands being purchased but not the income of the consumer, and wishes to

interact with consumers with high income. With help of the intuitive criterion (Cho &

Kreps 1987) Bagwell and Bernheim isolate the conditions under which some brands are

more expensive than others solely for signalling purposes.

5 Market demand with endogenous preferences

It is remarkable that Leibenstein reserves the term “Veblen effect” for the case where

demand depends on price, when it is the strand dealing with interdependent preferences

that reproduces Veblen’s results in a formal setting. Should we have a suspicion that the

10

same results will arise in the model where preferences depend on price?

This section will consider the implications of letting consumer preferences depend not

only on the amount of goods consumed, but also on price. We will investigate how robust

many of the traditional results of demand theory are, if consumers have preferences over

the price vector. For a reference to traditional results we will use Mas-collel, Whinston

and Greens ”Microeconomic analysis“ (1995) and Varians ”Intermediate microeconomics”

(1978).

5.1 Setting up the problem

5.1.1 The utility function

The problem we want to study can be expressed by the an assumption (following the

unconditional approach):

Assumption 1. The consumer has a continuous preference relation ′ %′ defined over all

pairs (x, p) ∈ R2n that is complete, reflexive and transitive.

Since the only prerequisite of the existence of a utility function is a continuous prefer-

ence ordering we can conclude that there exist a utility function that represents %. It is

intuitively clear that the introduction of price in the preferences does not affect the proof

of the existence of a utility function7, since utility is defined prior to any actual market

operations. We can therefore immediately conclude

Proposition 1. There exists a real-valued continuous utility function satisfying u(xA, pA) >

u(xB, pB)⇔ (xA, pA) � (xB, pB)

The only change we need to make to the monotonicity assumption is to make it con-

ditional on a price vector:

Assumption 2 (Monotonicity (for amounts)). For two commodity bundles xA, xB ∈ Rn

and a fixed price vector p ∈ Rn:

If xA � xB then xA � xB (1)

7For this proof see for instance Mas-Collel et al. Proposition 3.C.1

11

5.1.2 The utility maximization problem

Next we turn to the utility maximization problem of the consumer (UMP). Suppose there

is n goods:

maxx≤0

u(x, p) (UMP)

s.t. p · x ≥ w

Since this UMP is always done for a given price vector it doesn’t raise additional problems

that prices are included in the utility function. The necessary conditions for an optimum

(we assume an interior solution) for a consumer with income w are

∂u(x, p)

∂xi= λpi i = 1, ..., n (2)

n∑i=1

pixi = w (3)

where λ is the lagrange multiplier and can be interpreted as the marginal utility of money

for a given price vector.8 We define the demand correspondence x(p, v) (sometimes known

as Marshallian demand) to be the solution to this maximization problem.

5.1.3 The relative price assumption

Up till this point the exposition has contained nothing new compared to traditional choice

theory, but now we notice that the proof of the demand correspondence being homogeneous

of degree zero is no longer valid. Basically this proof says that for any scalar α the budget

sets B = {x ∈ R+ | p · x ≤ w} and Bα = {x ∈ R+ | αp · x ≤ αw} are identical and

consequently the utility maximization problem does not change. Obviously this proof is

invalid if prices enter the utility function, because the budgets sets are still identical, but

now the indifference curves will also shift.

This poses a problem for our exposition: It would be economically non-sensible for the

demand-correspondence not to be homogeneous of degree zero. It was not the intention

of including prices in the utility function to reach this “bizarre” result. The result would

imply that a consumer would have a different consumption pattern if she derives her utility

from prices in Euro rather than DKR. Therefore we will impose an additional assumption

8SOC: Given the assumption of monotonicity in amounts we can show that the determinant of the

bordered Hessian is not equal to zero and that u(x,p) is therefore indeed locally quasiconcave around

the solution to UMP for a fixed price vector. The sufficient conditions for a maximum is therefore also

fulfilled. (For proof see Mas-collel et al. p. 55 and mathematical appendix)

12

on the way prices influence preferences, saying that it is the relative rather than absolute

prices that influence utility.

Assumption 3 (Relative price assumption). For two different consumption bundles at

price vector p: (xA, p), (xB, p) ∈ R2n and any positive scalar α:

(xA, p) % (xB, p)⇔ (xA, αp) % (xB, αp) (4)

Note that this assumption implies, that we cannot assume monotonicity for prices.

Intuitively we would expect utility to rise if a given price rises, but claiming that a higher

price always makes the consumer better off is clearly in contradiction with assumption 3.

5.1.4 The expenditure minimization problem

With respect to the expenditure minimization problem (EMP) we have:

minx≤0

p · x (EMP)

s.t. u(x, p) ≥ u

Like in the UMP the necessary conditions for the expenditure minimization problem are

not very different from the traditional theory, as the consumer takes the prices as givens.

The first order conditions for this problem are (again we assume an interior optimum)9:

pi = λ∂u(x, p)

∂xii = 1, ..., n (5)

u(x, p) = u (6)

We define the fully compensated demand h(p, u) to be the solution to EMP and the expen-

diture function e(p, u) as the value function of EMP. That is, for a given utility u, h(p, u)

is the expenditure-minimizing bundle that achieves at least u, and e(p, u) = p · h(p, u) is

the minimum expenditure needed to achieve u. The reason for the term “fully” is that

following a price change we will compensate the consumer not only for the effect on her

budget set, but also the effect from the change of the indifference locus.

Once more we will need the relative price assumption 3 to guarantee that the fully com-

pensated demand is homogeneous of degree zero. Again the argument is, that given

assumption (3) the constraining function is identical for p and αp for any α. Since mini-

mizing the function p ·x is the same as minimizing p ·αx under this constraint the solution

is identical for all α. Likewise, in view of assumption (3) e(p, u) will be homogeneous of

degree one in p.

9For SOC see footnote 8

13

5.2 Invalidity of Shephard’s lemma

One of the major results of utility maximization theory deals with the relationship between

the compensated demand and the necessary expenditure. Within the cost minimization

problem of the firm it is referred to as “Shephard’s lemma” and since the expenditure

minimization problem is analogous this label is sometimes also used here. It states that:

hi(p, u) =∂e(p, u)

∂pii = 1, ..., n

It turns out that the main adjustments we need to make to the traditional theory in order

to include prices in the utility function comes from the fact that Shephard’s lemma is

not valid under price-dependent preferences. Most modern proofs of Shephard’s lemma

is a direct application of the envelope theorem to the EMP, but it can also be proved

by differentiating the expenditure function and applying the first order conditions from

the expenditure minimization problem. In both cases the proof rests on the fact that the

constraining factor, utility, is not dependent on prices. But that is exactly the exception

we are studying here and the proofs will be invalid. Since we want to fully compensate

the consumer after a price change we must take into account that the price change may

shift the indifference curves, which has an additional effect on the expenditure needed to

buy the old consumption bundle. Repeating the proofs of the lemma without assuming

the needed utility to be constant reveals an alternative (generalized) result. I will prove

it by first order conditions as this is most instructive of what is going on.

Lemma 1 (modified Shephard’s lemma). The compensated demand function is the deriva-

tive of the expenditure with respect to prices minus the change in expenditure needed in

order to achieve the prescribed utility due to the change in prices:

hi(p, u) =∂e(p, u)

∂pi− ∂e(p, u)

∂u

∂u(x, p)

∂pii = 1, ..., n (7)

or in matrix notation:

h(p, u) = ∇pe(p, u)− ∂e(p, u)

∂u∇pu(x, p) (8)

Proof. The expenditure function is by definition:

e(p, u) ≡ p · h(p, u) (9)

Differentiating this on both sides by pi yields

∂e(p, u)

∂pi=

∂

∂pi

n∑j=1

[pj · hj(p, u)

]=

n∑j=1

pj∂hj(p, u)

∂pi)+ h(p, u) i = 1, ..., n (10)

14

We insert the first order conditions (5) from the EMP pi = λ∂u(x,p)∂xi

in this equation:

∂e(p, u)

∂pi= h(p, u) + λ

n∑j=1

∂u(x, p)

∂xi

∂hj(p, u)

∂pi(11)

Now consider the constraint from (6) saying that the utility from the bundle solving the

EMP for a given p and u must necessarily be u:

u(h(u(x, p), p), p) = u(x, p) (12)

and differentiate this too with respect to pi:

n∑j=1

∂u(x, p)

∂xi

∂hj(p, u)

∂pi=∂u(p, x)

∂pii = 1, ..., n (13)

Inserting (13) into (11), rearranging and exploiting that λ is the gain in expenditure from

relaxing the utility constraint in the EMP for a given price vector(λ = ∂e(p,u)

∂u

)gives us

the result.

5.2.1 Implications of the invalidity of Shephard’s Lemma

This result allows us immediately to conclude that the substitution matrix given by

Dph(p, u) is not necessarily neither symmetric, nor negative semidefinite. Since the neg-

ative semidefiniteness is the mathematical expression of the law of demand, saying that

own-price effects on compensated demand are always negative we have also demonstrated

that the law of demand does not apply to demand with price-dependent preferences. With

price-dependent preferences we can therefore see upward-sloping demand curves - even in

the case with normal goods that have positive income effects. This can prove an alternative

explanation to the somewhat exotic Giffen good.

Proposition 2. With price-dependent preferences demand functions for non-inferior goods

can be upward-sloping.

5.3 The expanded Slutsky equation

The main result of this section is the expansion of the Slutsky equation with the appro-

priate generalisations to take account of price-dependent preferences. Having found the

modified version of Shephard’s lemma this task is straightforward. The proof is to be

found in appendix A.1.

15

Proposition 3 (Expanded Slutsky Equation). For all (p, w) ∈ Rn+1 and u = u(x(p, w), p)

we have

∂xi(p, w)

∂pj=

∂hi(p, u)

∂pj︸ ︷︷ ︸substitution effect

− ∂xi(p, w)

∂wxj(p, w)︸ ︷︷ ︸

income effect

+∂xi(p, w)

∂w

∂e(p, u)

∂u

∂u(x, p)

∂pj︸ ︷︷ ︸price-dependent utility effect

∀i, j (14)

It should be noted, however, that the income and substitution effects in the new Slutsky

equation is not the same as in the old Slutsky equation: In particular the substitution effect

can be negative. For discrete changes these effects can be illustrated by the help of figure

1. In this figure the movement from A to C is the substitution effect. At C the consumer

receives the same utility as in A, because the indifference curves have shifted with the

price change. The movement from B to D is the traditional income effect. This is the

effect that would arise if the consumer was not fully compensated, but instead was only

compensated for the change of purchasing power and not the change of indifference curves.

The total of these two effects does not produce the new demand, because the consumer

has to be fully compensated. This means that for a price increase we can withhold some of

the compensation, since the consumer can achieve the same utility with less income. This

amounts to the price-dependent utility effect which is the movement from C to B. The sum

of these effects is the total demand after a price change. Notice in this diagram C is to the

left of A, making the substitution effect negative as in the traditional theory. Furthermore

D is also to the left of A showing that the demand for good 1 is downward-sloping but, as

our above discussion shows, nothing makes this necessarily so.

6

-x1

x2

wp1

wp1

wp2

= wp2 @

@@

@@

@@

@@

@@

@@

@@

CCCCCCCCCCCCCCC

CCCCCCCCCCCCCCCCCC

CCCCCCCCCCCCCCCCCC

sss

s

A

B

CD

Figure 1: Effects of a price change with price-dependent preferences

16

5.4 Implications for market demand

Until now we have studied the inclusion of price in the utility function for a single consumer

taking price as a given. Insisting on exact terminology we have not yet touched upon

endogenous preferences, since price in this setting is not an endogenous variable. Only in

the case where price is determined by the demand of the consumers, which then feeds back

into the demand behaviour it is a case of endogeneity proper. But we can reason directly

from the partial analysis to the aggregate. If all consumers have the same demand the

aggregate demand curve will have the same properties as the demand curve for a single

consumer and we can infer market behaviour from the behaviour of the individual.

5.4.1 Arrow and Hahn’s result

Already in the famous book “General Competitive Analysis” which contains the proof of

the existence of a competitive equilibrium through a fixed-point point theorem it is briefly

remarked with explicit reference to Veblen and Scitovszky that this result is resistant to

including price in the utility function (Arrow & Hahn, 1971, p. 129-131) The traditional

proof 10 establishes that for any fixed price vector p and fixed utility maximizing bundles

x∗i (p, w) for all i at p, there exists a price vector p∗ that would support this allocation as

an equilibrium. The problem with including price in the utility function is that at p∗ the

bundles x∗i (p, w) need no longer be utility maximizing.

But Arrow and Kahn notices that there are no difficulties associated with adding p = p∗

as an extra equilibrium condition. The proof consists in applying a fixed point theorem

onto a map from relative prices into relative prices, with the prices increased of any goods

in excess supply. The form of this proof - a fixed point theorem - entails, that in an

equilibrium we will have both that utility is maximized for all consumers p, but also that

the price vector that supports this is p - otherwise p was not a fixed point. At the fixed

points the new equilibrium condition is fulfilled. All we need to do, therefore, is to adjust

the formulation of the proof, whereas the central idea of the proof is not affected. We can

conclude that there will exist a competitive equilibrium under price-dependent preferences.

5.4.2 Comparative statics

Above all, our conclusions are mainly negative, in the sense that we have showed the

invalidity of some of the basic claims of demand theory. The most remarkable result is,

that for price-dependent preferences the law of demand is not valid and normal goods can

10See for instance Varian p. 321

17

have upward sloping demand curves. We can call such goods conspicuous goods.

We now need to realize that it would be non-sensible for a consumer to have a demand

infinitely increasing in p. Due to his budget constraint, at some point the price will be so

high, that, even though the consumer will desire the good burningly, she can not afford

any of it, even if she dedicates her entire income to buying it. Demand curves can there-

fore only be upward-sloping for some segment of prices. Most probably upward-sloping

demand curves will be S-curved like depicted in figure 2, which is borrowed from Leiben-

stein. After point B the demand of the conspicuous good will start to fall even though the

6

-x1

p1 r rr

r

A

B

C

D

Figure 2: S-curved upward-sloping inverse demand curve

utility from consuming it is rising, because the effect from a tighter budget constraint will

exceed the increased utility from consuming it. From here on the demand curve will be

decreasing until it reaches point A, where the consumer has fully expanded her income on

the conspicuous good (if we assume the goods to be infinitely divisible the demand curve

will approach the axis as p→∞). It is reasonable to assume, even though we don’t need

to, that there is some lower p > 0 such that the good stops being conspicuous. Below point

C the good therefore acts as a normal good until point D, which can be interpreted as a

satiation point (if the consumer has no satiation point the demand curve will approach

the price axis as p→∞).

Now that we have the demand curve in place lets suppose supply of the conspicuous

good is fixed; making the supply curve vertical. This means that whenever the supply

curve cross the upward sloping part of the demand curve it will also cross the demand

curve in an upper and a lower point where demand is downward sloping - making three

equilibrium prices (if there is no p under which the good stops being conspicuous there

will only be two). If we suppose equilibrium is found by a process of tatonnement then

we can be tempted to use the lingo of differential equations and call the equilibrium on

the upward sloping part unstable - we should not expect to find this equilibrium in the

18

economy. Suppose there is a small upward perturbation in prices at the equilibrium point

- this will increase demand for the conspicuous good thereby calling for a higher price,

which will lead to an additional increase in demand and so on - moving the price level

away from the upward sloping part until it reaches the new equilibrium at the higher price.

For an ordinary upward-sloping supply curve crossing the upward sloping part there is two

options. If the demand curve crosses the upward sloping part from below there will be at

least three crossings of the demand curve and the equilibrium on the upward-sloping part

will be unstable like before. The only possibility of a stable equilibrium on the upward

sloping part is when the supply curve cuts the demand curve from above - in this case we

will see that for a perturbation making the price higher than the equilibrium price there

will be excess supply and the process of tatonnement will move price back into equilib-

rium. This will happen because the volatility of supply with respect to price is greater

than effects from conspicuousness and therefore the increased supply stops the feedback

effect in prices.

Notice that the result from Hopkins & Kornienko found is not reproduced for price-

dependent preferences. We cannot say, that as society gets richer consumers will devote

a still larger part of their resources to the price-dependent good. Rather we can say that

as society gets richer, and provided this leads to an increase in the relative price of the

conspicuous good (which we cannot say), then there will be a sudden jump in the price -

making all of the conspicuous effect visible within a very short period of time (this could

be envisioned as the jump to a new brand of an identical good with a much higher price).

After this jump the demand for the good will again be negatively dependent of price since

the resource constraint is now binding.

6 Welfare with endogenous preferences

The reader of this paper has perhaps by now become suspicious that where endogenous

preferences will contrast with the traditional microeconomic theory is not so much within

the area of market demand, but rather in the area of welfare. It is a big and relevant

question whether traditional welfare theory can be upheld if preferences are endogenous.

We have already seen that Scitovszky feared the “havoc it may wreak with the whole

theory of choice”. Arrow and Hahn notices within the unconditional setting of price-

dependent preferences that “the significance of Pareto efficiency becomes obscure, since

an allocation that is dominated at one set of prices is not dominated at another” (Arrow

and Hahn 1971).

19

In this way there seems to have been an understanding among those that have written

within the field that the concept of Pareto efficiency is invalidated in models of endogenous

preferences. Mark Blaug in “Economic Theory in retrospect” also lists the absence of

interdependent preference as one out of three assumptions underlying Pareto efficiency as

a normative concept 11. In a quote summing up the issue C.C von Weizsacker notes:

One of the reasons why economists did not very deeply discuss this question

may be that their present concepts of Pareto optimality is not flexible enough

to cope with endogenously changing tastes. It may become necessary to change

the conceptual framework of our theory; we may be forced to ask almost philo-

sophical questions about the concepts we use. (von Weizsacker p. 345)

The problem that these writers perceive cannot be that the consumers are not utility max-

imizing, since this is a fundamental feature of the model - the Pareto criterion is therefore

not invalidated by strict definition. Neither is the probelem that the model with exoge-

nous preferences misestimates the effect of endogeneity in real life by assuming them away,

because that could in principle be corrected by incorporating the effects into our model

(as I have tried to do in this paper). The problem seems to be, that confronted with the

issue of endogenous preferences we begin to doubt one of the fundamental assumptions of

welfare theory: Namely the identification of welfare with the satisfaction of preferences.

You could for instance imagine, as Blaug tells us to, a situation in which a new product

is introduced into a market. Because preferences are independent the product may be

bought by everyone else simply because others are buying it. If this is the sole reason

everyone is buying no one would be worse off if the product was withdrawn from the

market (Blaug 1997). Pollak drives the point home:

Variable tastes undermine the normative significance of welfare economics

which asserts (in a precise sense and under fairly stringent assumptions) that

in a competitive equilibrium everyone gets what he wants [...] However if

tastes are sufficiently malleable then this may be no more than corollary to the

general proposition that people come to want what they get (Pollak 1978).

Notice that to make an analogous argument in relation to the model presented in this

paper would have to assume that the utility derived from a high price doesn’t count. That

11the second being that the individual is the best judge of his own welfare and the third the incompa-

rability of individual welfare

20

utility is not maximized in equilibrium is not the source of the problem. Rather it seems

somehow that when people maximize an endogenously determined utility function it is

not their “true” welfare that they are maximizing. This forces us to raise those “almost

philosophical questions” that von Weizsacker referred to above. A quick look within

the doors to the philosophy department, where philosophers discusses ethical theories of

whether personal welfare can be said to be satisfaction of preferences is often enough

to make even the most hardened economist run back to his graphs and equations. It is

definitely beyond the scope of this paper.

7 Conclusion

Despite the massive amount of everyday anecdotal evidence for the existence of endoge-

nous preference effects in real-world economic situations this has received surprisingly little

attention within economic theory. Among those who have tried to predict the effects of

endogenous preferences on market demand, many have been able to find results already

envisioned by Veblen. This is true for instance for modellings of interdependent prefer-

ences. These models suggests that the welfare of individuals is negatively dependent on

the average income in society and that positional goods tend to crowd out other goods.

Leibenstein has suggested that “Veblen effects” is best characterised by effects where the

demand for a good depends on the price of the good (Leibenstein 1950), but this paper

shows that this is actually misleading. A model with price-dependent preferences does not

smoothly reproduce the results Veblen had predicted. The effects imagined in the actual

work of Veblen is rather in line interdependent preferences.

Instead the model with price-dependent preferences predicts other results, which have

so far been unexplored. We have shown that as economic parameters changes continu-

ously, and thereby determines continuous demand and supply behaviour, we can nonethe-

less observe non-continuous price jumps as a good moves from being non-conspicuous to

conspicuous. Furthermore we have shown the analytical possibilities of distinguishing a

“price-dependent utility income effect”. Certainly many other interesting results can be

produced by following this approach.

By briefly touching upon the welfare effects of endogenous preferences we have seen, that

research in this area risks opening a box of Pandora, leading to a vast array of philosophical

discussions about the most fundamental concepts of microeconomic theory. This would be

another possibility for continued research into the implications of endogenous preferences.

21

References

[1] L. S. Bagwell and B. D. Bernheim, Veblen effects in a theory of conspicuous

consumption, American Economic Review, 86 (1996), pp. 349–73.

[2] M. Blaug, Economic theory in retrospect, Cambridge University press, Cambridge,

5th ed., 1997 (1962).

[3] S. Bowles, Endogenous preferences: The cultural consequences of markets and other

economic institutions, Journal of Economic Literature, 36 (1998), pp. 75–111.

[4] I.-K. Cho and D. M. Kreps, Signaling games and stable equilibria, The Quarterly

Journal of Economics, 102 (1987), pp. 179–221.

[5] J. S. Duesenberry, Income, Saving and the Theory of Consumer Behavior, Harvard

University Press, Cambridge, 1949.

[6] B. C. Eaton and M. Eswaran, Well-being and affluence in the presence of a veblen

good, Working Papers 2008-12, Department of Economics, University of Calgary, Feb.

2008.

[7] M. Friedman, Price theory, a provisional text. Aldine, Chicago, 1970.

[8] H. Gintis, Alienation and power towards a radical welfare economics (quoted from

hanhnel and albert (1990)), Master’s thesis, Harvard University, 1969.

[9] R. Hahnel and M. Albert, Quiet Revolution in Welfare Economics, Princeton

University Press, Princeton/Oxford, 1990.

[10] F. Hirsch, The Social Limits to Growth, Routledge Kegan Paul, London, 1976.

[11] E. Hopkins and T. Kornienko, Running to keep in the same place: Consumer

choice as a game of status, American Economic Review, 94 (2004), pp. 1085–1107.

[12] P. J. Kalman, Theory of consumer behavior when prices enter the utility function,

Econometrica, 36 (1968), pp. 497–510.

[13] H. Kenneth J. Arrow, F. H., General Competetive Analysis, Holden Day, San

Fransisco/Edinburgh, 1971.

[14] H. Leibenstein, Bandwagon, snob and veblen effects in a theory of consumers’

demand, The Quarterly Journal of Economics, 64 (1950), pp. 183–207.

22

[15] A. Marshall, Principles of Economics, Macmillan, London, 1920.

[16] A. Mas-Colell, M. D. Whinston, and J. R. Green, Microeconomic Theory,

Oxford University Press, New York/Oxford, 1995.

[17] P. Pashardes, Myopic and forward looking behavior in a dynamic demand system,

International Economic Review, 27 (1986), pp. 387–97.

[18] A. C. Pigou, The Economics of Welfare (quoted from Leibenstein (1950)), Macmil-

lan, London, 1935 (1920).

[19] R. A. Pollak, Habit formation and dynamic demand functions, Journal of Political

Economy, 78 (1970), pp. 745–63.

[20] , Interdependent preferences, American Economic Review, 66 (1976), pp. 309–20.

[21] , Price dependent preferences, American Economic Review, 67 (1977), pp. 64–75.

[22] , Endogenous tastes in demand and welfare analysis, American Economic Review,

68 (1978), pp. 374–79.

[23] J. Rae, The Sociological Theory of Capital, Macmillan, 1905.

[24] L. Robbins, An essay on the nature and significance of economic science, Macmillan,

London, 1932.

[25] T. Scitovszky, Some consequences of the habit of judging quality by price, The

Review of Economic Studies, (1944).

[26] F. Spinnewijn, Rational habit formation, European Economic Review, 15 (1981),

pp. 91–109.

[27] G. J. Stigler and G. S. Becker, De gustibus non est disputandum, American

Economic Review, 67 (1977), pp. 76–90.

[28] H. R. Varian, Microeconomic Analysis, Norton, New York/London, 3rd ed., 1992

(1978).

[29] T. Veblen, The theory of the leisure class, in Collected Works of Thorstein Veblen,

Routledge, 1992 (1899).

[30] C. C. von Weizsacker, Notes on endogenous change of tastes, Journal of Economic

Theory, 3 (1971), pp. 345–372.

23

A Appendix

A.1 Proof of the expanded Slutsky equation

Proof. From duality we know the relationship between Marschallian and fully compensated

demand to be:

hi(p, u) = xi(p, e(p, u)) (15)

Differentiating this equation with respect to pj gives us:

∂hi(p, u)

∂pj=∂xi(p, e(p, u)

∂pj+∂xi(p, e(p, u))

∂w

∂e(p, u)

∂pj∀i, j (16)

Using the modified Shephard’s lemma this is:

∂hi(p, u)

∂pj=∂xi(p, e(p, u)

∂pj+∂xi(p, e(p, u))

∂w

[hi(p, u) +

∂e(p, u)

∂u

∂u(x, p)

∂pj

]∀i, j (17)

Rearranging and using from duality that e(p, u) = w and h(x, p) = x(p, w) gives new the

Slutsky equation

A.2 Quote from Nationaløkonomisk Tidsskrift

Quote from “Nationaløkonomisk tidsskrift” year 1951. P. Nørregard Rasmussen reviews

“James S. Dusenberry: Income, Saying and the Theory of Consumer Behavior, Harvard

University Cambridge, Mass,, 1949. 128 sider’ (Price: 2.50 $)”

For at forklare dette (RED: the Kuznet-puzzle), gar D. tilbage til den almin-

delige efterspørgselsteori og hæfter sig her ved det forhold, at den er udviklet

ud fra en forudsætning om, at der ligger individuelle behov bag efterspørgslen

til forbrug. Man har dermed overset, at der fuldt sa meget er tale om et socialt

behov. [...] Om det lykkes, ikke alene at holde forbruget sa langt nede, at

indkomsten slar til, men tilmed at have en positiv opsparing, bestemmes først

og fremmest af miljøet. Primitivt udtrykt, ma man — og vil hellere end gerne

— hyle med med de ulve, man er iblandt, og man bliver rasende misundelig

hvis man ikke kan gøre det.

24