The bias generated by the subjective perception of scarcity on the consumer's choice is discussed from a theoretical perspective. The core idea here discussed is that scarcity is an Lancasterian attribute of the goods which is not endogenously built in the goods, like many physical attributes, color, weight, etc. but which is dependent from the context where the good is consumed. The exogenously nature of scarcity requires a specific theoretical treatment which is here attempted

Ivan Soraperra

Luigi Mittone

English

Research Papers in Economics

The Scarcity Bias: Some Theoretical Notes 
 
DRAFT VERSION 
 
LUIGI MITTONE 
Department of Economics, University of Trento, Via Inama 5, 38100, Trento, ITALY 
luigi.mittone@unitn.it 
 
IVAN SORAPERRA 
CEEL, University of Trento, Via Inama 5, 38100, Trento, ITALY 
 
 
Abstract 
 
The  bias  generated  by  the  subjective  perception  of  scarcity  on  the  consumer’s  choice  is  discussed  from  a 
theoretical perspective. The core idea here discussed is that scarcity is an Lancasterian attribute of the goods which 
is not endogenously built in the goods, like many physical attributes, color, weight, etc. but which is  dependent 
from the context where the good is consumed. The exogenously nature of scarcity requires a specific theoretical 
treatment which is here attempted. 
 
Keywords: Scarcity, Decision-making, Economic behavior, Economic theory 
 
 
 
1. Introduction: back to Adam Smith 
 
This paper takes the hint from two empirically based ones (Mittone, Savadori and Rumiati, 
2005, Mittone, Savadori, 2006)
1 and examines the attraction effect produced by scarcity on the 
consumer behavior theory. More precisely what is investigated here has nothing to do with the 
so called Veblen’s effect (Veblen, 1899/1965) and therefore we are not specifically interested 
to study the properties of the demand of some special categories of luxury goods (who someone 
calls ostentation goods). 
What is here analyzed is a more general phenomenon which is related to the psychological 
role played by the perception that a normal good is a scarce one, given the place and time 
where and when is consumed. It is important to underline that what matters here is not the real 
availability of a good but the perception that the consumer has of the local amount of a given 
good at disposal for consumption. From now on the term “scarcity” has to be considered as a 
synonymous of “subjectively perceived scarcity” and that the perception of scarcity is linked to 
the belief that in a given moment in time and in a specific place a given good is scarce.  
                                                 
1 This introduction is partially taken from Mittone, Savadori and Rumiati (2005).   2 
A  better  way  to  describe  the  specific  definition  of  scarcity  discussed  here  is  to  use  the 
consumer theory developed by Kelvin Lancaster (1966a, 1966b). As well known the theory by 
Lancaster can be considered as part of a wider theoretical frame the so called New Household 
Theory  (NHT  thereafter)  which  represents  an  attempt  (around  the  sixties  and  seventies)  to 
overcome one of the weakest point of the neoclassical theory of consumption, that is to say the 
assumption of stable and given preferences. Even if the building of NHT is the result of the 
work of other Authors (in particular of Becker, 1965) the part of NHT which is relevant here is 
related to the special assumption made by Lancaster with respect to the nature of the goods. 
Lancaster assumes that the purchased goods enter in the consumer’s utility function as sets 
of  characteristics  produced  by  the  goods  themselves.  In  other  words  the  consumer  is  not 
interested to the goods but to the services that she can obtain from their use. In this sense the 
majority  of  the  characteristics  of  goods  can  be  considered  as “intrinsic”  or  “stable”.  From 
apparently different goods (e.g. a car and an airplane ticket) the consumers can extract the same 
service  (in  the  example  of  the  car  and  of  the  airplane  ticket  the  service  is  transportation) 
together with other services which can be completely different. From the car the consumer can 
extract the pleasure of driving (if she likes to drive), while this is not possible with the airplane 
ticket, vice versa with the airplane ticket the consumer can obtain also the pleasure to fly (if she 
likes to fly). 
Using the same definition of goods suggested by the Lancaster’s theory helps to clarify why 
scarcity is a so peculiar characteristic. Most of the attributes of a good in the Lancasterian 
approach are intrinsically built in the good itself. More precisely to be intrinsic means that a 
specific set of attributes is embodied in  a given good independently from the context where the 
good is purchased and consumed. The attribute of scarcity, conversely, is not intrinsic but it is 
context-dependent. To know if a good owns the scarcity attribute, that is to say to know if it can 
be considered scarce or abundant, a consumer needs to know its “local” availability, whereas to 
know the presence-absence of a generic attribute (for instance the color) a consumer needs only 
information relative to the good itself and not to the environment. Moreover, to perceive the 
degree of scarcity the consumer often needs to know the level of competition on the demand 
side. To know the total availability of a good can be not enough because the consumer can 
perceive it as scarce – independently form the total amount of that good existing in nature – 
because she knows that many other consumers wish that good. 
To  look  for  some  preceding  reference  to  the  role  of  scarcity  in  the  explanation  of  the 
consumer behavior means to go back to Adam Smith and to his distinction between “value in 
use”  and  “value  in  exchange”.  To  explain  the  difference  between  these  two  concepts  he   3 
presented the famous paradox of diamonds and water. As well known the diamonds and water 
paradox tells that even if water is very useful it is also generally very cheap while diamonds 
have little if none utility  but they are very  expensive. From this paradox Smith arrived to 
conclude that the willingness to pay does not depend from the degree of usefulness of the 
goods, i.e. he argues that the value of goods is not influenced by their characteristics but by 
some other mechanism, in his words: “the merit of an object, which is in any degree either 
useful  or  beautiful,  is  greatly  enhanced  by  its  scarcity”  (Smith  1776,  p.172).  It  is  worth 
noticing that the Smith’s sentence underlines a sort of ante littera behavioralism because it 
links in some way the preferences building process to the perception of a specific attribute – 
scarcity – .  
In the Smith’s paradox we can find both the sources of scarcity: context dependent scarcity – 
linked to the Smith’s definition of value in use – and demand competition scarcity – which is 
related to the value in exchange –. Water can assume the scarcity attribute because in a given 
moment in time and in a given place in space (e.g. in a desert) it is a very limited resource. In 
spite of the fact that the absolute value in use has not changed water becomes very valuable in 
the desert independently from the consumer’s need. In fact at a given moment in time the 
consumer can be perfectly fine in the desert because she does not feel any need to drink. Still 
she will surely attribute a much higher value to a liter of water in the desert than to the same 
liter of water when staying on the border of an alpine lake. 
On the other side the scarcity attribute for diamonds is almost totally due to the pressure 
exerted by the demand competition. Diamonds are not scarce in absolute terms (as a matter of 
fact they are relatively abundant in nature) but they are highly demanded and therefore they 
become scarce assuming an high value in exchange. The consumer can be totally uninterested 
to diamonds by themselves because she cannot extract any utility from them – she simply does 
not like diamonds – but still she will attribute a high value to a diamond. The value subjectively 
attributed by the consumer to a diamond would be high either because she is aware that it is a 
“rare” commodity – “the merit of an object,…., is greatly enhanced by its scarcity” – and 
because she knows that diamonds are an highly requested commodity and therefore she knows 
that she could extract value by exchanging it on the market. 
About one century after the Wealth of Nations (1776) the Adam Smith’s paradox has been 
attacked by the Neoclassical economists. The concept of marginal utility allows in fact to re-
link the value of goods to utility and to explain why a consumer will pay one carat of diamonds 
millions times the price of a gallon of water. As well known the idea embodied in the marginal 
concept utility is that the value attributed to a given commodity by a consumer is determined by   4 
the ratio between the total utility that s/he obtains from the amount of the good already owned 
and  the  amount  of  utility  that  s/he  can  extract  from  an  additional  unit  of  the  good  itself. 
Through an apparently simple mechanism of comparison among the marginal utilities divided 
by the price of each good the consumer should then arrive to determine her/his willingness to 
pay for each amount of every existing good. The relative scarcity/abundance of a given good is 
in some way “embodied” in the objective characteristics of the goods itself through the market 
price and becomes a non relevant element for the consumer when she builds up her preference 
maps. 
In spite of the fact that neoclassical economists are almost totally miser in explaining from 
where  preferences  come  from  it  seems  reasonable  to  think  that  the  preferences  building 
mechanism that they have in mind should be linked in some way to the strength of the needs or 
wishes that the consumer feels for each specific good. This means that the high value attributed 
to water in the desert should be due to a strong thirst or to the forecast of a future extreme need 
of water. Then the amount of water that the consumer will actually buy will depend by the price 
of water (in the desert), by her budget constraint and by all the other needs she must cope with 
(and by the prices of the other goods). In this sense to know if water is scarce or abundant is not 
relevant and in any case does not matter for building up the preferences map which broadly 
depends only from individual needs. 
Similarly also the value attributed to diamonds by the consumer in the neoclassical view 
should be a consequence of the wish to own a beautiful thing (which is a cultural as well as a 
physical attribute of diamonds themselves) or to own something that can be re-sold in the 
future (un-material attribute).  Once again the amount of diamonds purchased by the consumer 
is only a matter of budget constraint and prices. 
A  point  of  weakness  of  the  Neoclassical  solution  of  the  Smith’s  paradox  relies  on  the 
implicit assumption that the preferences structure of the consumer cannot be influenced by the 
relative local disposable amount of each commodity. Telling it in a different manner this means 
that the level of utility that the consumer can obtain from a given good is independent from the 
amount of the good existing in nature. Vice versa when this is not the case the marginal utility 
loses  its  property  of  “stable”  measure  of  the  willingness  to  pay  because  utility  becomes 
dependent from the amount of the commodity existing in nature. It emerges a system of double 
interaction  between  the  preferences  structure  and  the  quantity  of  the  good  in  nature.  This 
double system can generate modifications in the standard properties of the utility surface. 
Finally for a sake of completeness it is worth remembering that from a macro perspective in 
the neoclassical world scarcity simply does not matter (one could say does not exists) because   5 
the market would provide to automatically re-adjust the local availability of any possible good 
through the general equilibrium. The physical re-distribution of goods is ensured by the price 
mechanism combined with the interconnections among local markets. From the neoclassical 
perspective scarcity of water in the desert is not a state of nature: it is only a consequence of the 
market. Las Vegas is in the middle of a desert but water is abundant as is in almost any other 
US towns. 
The point here is not to argue on the neoclassical treatment of the attribute of scarcity while 
to discuss on the psychological effect produced on consumer behavior by the perception that a 
given good owns the attribute of scarcity. It is important to remember that we are here speaking 
of  perceived  scarcity  and  not  of  “real”  scarcity.  More  precisely  we  are  interested  to  the 
attractive mechanism  put forth by the attribute of scarcity on consumer choice. 
 
 
2. A parametric model of scarcity 
 
In the introduction we anticipated that we shall restrict ourselves to treat only the case of 
subjectively perceived scarcity linked to a contextual effect. We move from two hypotheses: 
H1) the consumer feels a psychological attraction for all those goods which she perceives as 
scarce in nature, this means that her utility level is influenced by the pleasure to consume a 
scarce good; 
H2) the “state of nature” which determines the relative availability of a given good is strictly 
local and temporarily limited to a given moment in time, e.g. time t0 (the state of the world here 
and now). 
A possible way to cope with the theoretical treatment of the consumer behavior when there 
is a good characterized by scarcity is to use a specification of the utility function able to take 
into account the relationship between utility and the perceived amount of the good existing in 
nature. 
The utility function of equation 2.1 models a consumer whose utility depends directly on the 
quantity consumed  y
c Q of a scarce good y and inversely on the total amount of y existing in 
nature  y
e Q . 
 
y
e
Q
Q
U
y
c
+
-
=
-
1
æ 1
          [2.1]   6 
 
 
The utility surface reported in fig. 2.1. has been obtained by computing equation 2.1 in the 
arbitrarily chosen parametric space for 0 ≤  y
c Q  ≤ 10 and  0 ≤  y
e Q  ≤ 10.  
 
Fig. 2.1 Utility surface 
0
2
4
6
8
10
Qe
0
2
4
6
8
10
Qc
0
0.1
0.2
0.3
U
0
2
4
6
8
Qe
 
 
The utility surface of fig. 2.1 is referred to a good (y) which has two Lancasterian attributes: 
an endogenous one and a context dependent one. The endogenous attribute refers to “standard” 
characteristics  of  goods  like  colours,  weight  and  so  on.  The  context  dependent  attribute 
(scarcity) gives the consumer a level of utility which depends inversely on the amount of the 
good existing in nature. Due to the effect produced by the standard attribute, an increase in the 
amount of the quantity consumed (Qc axis) increases utility, following the standard law of 
decreasing marginal utility. Instead, an increase in the quantity of the good existing in nature 
causes a variation in the marginal utility which depends on the specific parameterization chosen 
for the function 2.1. More precisely, the higher the psychological value given to scarcity and 
the lower the amount of the good in nature (Qe axis), the higher the level of utility obtained. 
Cutting the utility surface at a given value of Qe we obtain the graph of fig. 2.2.   7 
In fig. 2.2 the horizontal axis reports the amount of quantity consumed while the vertical 
axis measures the level of utility. To each level of the utility curves corresponds a different  
degree  of  scarcity  which  means  that  higher  utility  curves  match  up  lower  amounts  of    y 
available in nature. It is also worth noticing that the shape of the utility curves of fig. 2.2 is 
coherent with the decreasing marginal utility law, as already anticipated. 
Fig. 2.2   Longitudinal section (Qc axis) of the utility surface 
 
2 4 6 8 10
0.1
0.2
0.3
0.4
0.5
 
 
 
The  graph  shown  in  fig.  2.3  has  been  obtained  by  fixing  a  given  amount  of  quantity 
consumed (the vertical  axis measures the utility level  while the horizontal axis reports the 
amount of a given good existing in nature). The graph shows the relationship between the 
utility level and the quantity of y existing in nature. The scarcity effect reduces the total utility 
gained by the consumption of y as the amount of y existing in nature increases 
 
 
 
 
 
 
 
 
 
 
   8 
Fig. 2.3 Relationship between utility and scarcity 
0.5 1 1.5 2
20
40
60
80
100
 
 
 
Finally the graph reported in fig. 2.4 shows the relationship between utility (always reported 
on the vertical axis, while the horizontal axis reports the total quantity of y existing in nature) 
and the amount of y consumed by the consumer accordingly with the overall quantity of y 
owned  by  the  consumer  herself.  The  two  curves  show  respectively  a  situation  where  the 
consumer holds 100% of the good existing in nature – higher curve – and a situation where the 
consumer owns only the 20% of the total quantity of y. It is worth noticing that increasing the 
quantity of y consumed also the utility level increases but this positive relationship worth until 
y remains in the scarcity region (idem est until there are only few units of y available in nature).  
The curves of fig. 2.4 demonstrate the existence of a “destruction paradox”, which means that 
for the consumer could be rational to destroy the good that she holds because in this way she 
increases the fraction of total utility generated by scarcity more than the relative loss in utility 
caused by the reduction of the quantity consumed. When the consumer holds the total amount 
of the good the shape of the utility curve does not change but the relative steepness decreases 
and the destruction paradox loses its strength. 
 
 
 
 
 
 
 
 
 
   9 
Fig. 2.4 The destruction paradox 
 
2 4 6 8 10
0.05
0.1
0.15
0.2
0.25
0.3
 
 
 
 
 
3. Conclusions 
 
The theoretical exercise here tried cannot be considered conclusive for two reasons: first 
because is based on a parametric approach and therefore cannot be generalised, second because 
the mathematical properties of the model have not been completely discussed.  
More  precisely  the  results  that  we  have  obtained  are  closely  related  to  the  hypotheses 
introduced in the model. The first hypothesis is that the first derivative, with respect to the 
quantity  consumed,  must  be  positive  and  the  second  derivative  must  be  negative,  –  and 
accordingly with the standard theory – the second hypothesis is that the first derivative, with 
respect to the quantity available in nature, must be lower than zero and the second derivative 
must be greater than zero. Given these assumptions the level of utility which depends from 
scarcity – i.e. which depends from the amount of the good existing in nature – decreases with a 
relative lower degree as the amount of the good existing in nature increases. 
Unfortunately  we  have  not  verified  the  partial  derivatives  and  therefore  we  cannot 
generalize  the  results  obtained  with  particular  concern  with  the  paradox  of  destruction. 
Nevertheless the model shows the existence of at least one example of the paradox, conditioned 
to the specific parameters chosen in the model. 

The Scarcity Bias: Some Theoretical Notes

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The Scarcity Bias: Some Theoretical Notes

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