optimal sequential search and optimal consumption-leisure choice
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From the SelectedWorks of Sergey Malakhov
September 2011
Optimal Sequential Search and OptimalConsumption-Leisure Choice
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1
Sergey Malakhov
Ph,D, Applied Economics,
Pierre Mendes France University,
Grenoble, France
To F&F
Optimal Sequential Search and Optimal Consumption-Leisure Choice
Abstract
In this paper we introduce the model of consumption-leisure choice where marginal costs and
marginal benefit of search support maximization of current consumption – leisure utility as well
as maximization of monetary reserve for future purchases. Despite its algebraic simplicity, the
model, presented in this paper, reflects many important considerations of different studies on
search behavior. But methodologically the model follows the economic approach developed by
G.Stigler and G.Becker who transformed once a commonsense idea, that leisure is not equal to
the time away from work, into fundamental theoretical concepts. The model also incorporates
some intriguing theoretical issues of J.Stiglitz’s work on self-selection. Following the “de
gustibus non est disputandum” maxim, the paper accentuates the methodological role of
marginal rate of substitution of leisure for consumption in decision-making process. But this way
redirects the study of search behavior towards an idea of relative sufficiency in consumption,
accompanied by buffer-stock saving behavior. The model also activates time horizon of
consumption – leisure choice in unconventional manner and it shows how observable time
horizon of consumption – leisure choice changes MRS (H for Q). The economic approach to
relative sufficiency in consumption gives a green light to review the problem of relativity of
utility as well as H.Simon’s search-satisficing concept. Finally, the analysis of polar models of
behavior, Veblen effect and PWE, illustrates how economic attributes of the model can explain
ethical aspects of economic behavior.
JEL Classification: D01, D11, D83, D91.
1. Reserve for Future Purchases
Suppose that the general relationship between benefits and costs of search is given by
2
R(S) = wL(S) – QP(S), where
wL(S) – labor income wL lost during search S (∂L/∂S <0)
QP(S) – expenditures on fixed or pre-allocated quantity (∂P/∂S<0)
R(S) – reserve (saving) for future purchases.
Saving for purchases occupies an important niche in hierarchy of financial needs. (Xiao, J.J.,
Noring,F.E (1994)). It can be considered as simple, short-term form of precautionary motive,
because “in reality purchases are made sequentially, some frequently and some infrequently, so
that while the purchaser has exact up-to-date information about the prices of the goods actually
being bought, he does not have accurate knowledge of the prices of other goods.” (Deaton, A.
(1977, p.899)).
Search for lower price continues until marginal benefit equals the value of marginal costs, or
)1(S
Lw
S
PQ
When consumer ends up the search, he maximizes reserve for future purchases (Fig.1):
)2()()()(0***
SQPSwLSRRwhereS
R
S
PQ
S
Lw
This is a real maximum. A diminishing marginal utility of labor leaves for search less productive
hours and, with regard to search, it gives us ∂2L/∂S
2<0. But marginal utility of search itself is
also diminishing, or Q∂2P/∂S
2 >0. Finally, ∂
2R/∂S
2=w∂
2L/∂S
2 - Q∂
2P/∂S
2<0.
Fig.1.
R(S*)
wL(S)
R(S) ; QP(S) ; wL(S)
QP(S*) QP(S)
wL(S*)
S* S
3
If reserve for future purchases is based on precautionary motive, consumer doesn’t need liquidity
constraint, because “the precautionary saving motive essentially induces self-imposed reluctance
to borrow (or to borrow too much.)” (Caroll, C.D., (2001, p.32)). Even if we borrow and the
reserve becomes negative, we try to equalize marginal benefit of search with its marginal costs,
this time in order to minimize the deficit.
2. Consumption – Leisure Choice
When consumer has no liquidity constraint he can optimize current consumption – leisure choice
(Q,H) with respect to equality of marginal values of search. So, the individual’s objective is to
maximize consumption – leisure utility U(Q,H) subject to the constraint
)3(/
/
SL
SPQw
Setting the Lagrangian expression ./
/(),(
SL
SPQwHQU
) , the first-order conditions
for a maximum are:
0/
/
;0/
/
HSL
SP
QH
U
HSL
SP
Q
U
Q
Trying to determine the marginal rate of substitution of leisure for consumption, we get1:
1 We take the value ∂P/∂S as given by price dispersion of local market. If we presuppose that an individual can
always adjust price reduction to pre-allocated quantity (∂P/∂S=∂P/∂S(Q)) and to target leisure time
(∂P/∂S=∂P/∂S(H)), consumption and leisure become perfect complements. The model implies that consumer can
choose a market with certain price dispersion, but he is still price-taker there, now price-reduction-taker.
4
)4(//
)(/
/
//
;//
)/(/
/
//
/
/
/
/
/
/
2
2
2
2
HSLSP
wHforQMRS
QU
HU
SP
w
SL
Q
S
Lw
S
PQ
HSLSL
Q
SLSL
SP
HSLSPQ
SL
SPH
SL
SPQ
QU
HU
If we differentiate the value of consumption Q with respect to leisure directly, we get the same
result, which facilitates geometrical interpretation of the model.
)5()(
,///
/ 2
HforQMRSH
Q
orHSLSP
w
H
Q
SP
SLwQ
We can see that the classical model of individual labor supply represents only a particular case of
the model presented here. When markets are almost perfect and/or consumer is well informed,
time of search approaches to zero (S→0; ∂P/∂S→0;∂L/∂H→-1), and we have:
)6()1
())(
)(
(lim
)/
/(lim)
/
/(lim)(lim
0
2
0
2
00
P
w
Pw
SP
SH
L
w
SP
SHLw
SP
HSLwHforQMRS
S
SSS
The reserve maximization model comes closely to buffer-stock concept of saving behavior.
Indeed, if MRS (H for Q) approaches to w/P ratio, consumer spends all disposable income on
current consumption. But the uncertainty of present and future price dispersions activates search
process and creates reserve for future purchases. And "the expected savings from given search
will be greater, the greater the dispersion of prices.” (Stigler,G. (1961, p.215))
Finally, the model exposes time horizon of consumption-leisure choice, which is presented in the
classical labor supply model only implicitly. If we denote
)7(24
24)(
HH
S
L
S
L
5
we get ∂2L/∂S∂H = 1/24 =1/T, where the value T represents time horizon of consumption-leisure
choice.
Therefore, we can present budget constraint in linear form:
)8(24
24
//
/ 0
0000
000
H
SP
w
SP
SLwQ
Now we can present graphical illustration of consumption-leisure choice (Fig.2):
Fig.2
3. Absolute propensity to search
If we differentiate T = L(S)+H(S)+S with respect to S, we have
∂L/∂S+∂H/∂S+1 =0. (9)
We can see how the value ∂L/∂S becomes critical for different models of behavior. Taken in
absolute terms, it gives us an absolute propensity to search |∂L/∂S|. This value exposes our
willingness to substitute labor for search. Here we simply assume, that “some individuals are
more averse to work than others.”(Stiglitz, J.(1982, p.233)). But at the same time the value of
absolute propensity to search depends on leisure time that we are willing to trade away to get an
aspiration level of consumption.
6
When we decide to stop the search, we take into consideration alternative use of time – either to
work a little bit more and to increase our chances for bonus, or to enjoy our leisure. The latter
feeling is more common. But it determines automatically the value ∂H/∂S, which in the same
manner, automatically, due to ∂L/∂S + ∂H/∂S + 1 = 0 rule, determines the value of propensity to
search ∂L/∂S, if we really have a chance to get bonus for extra hours or we decide to spend extra
hours in office to improve our skills.
The key equation (1) of the reserve maximization model explains how different propensities to
search ∂L/∂S equalize different intensities of consumption (Q;H) with different values of price
reduction ∂P/∂S.
From (1) we can see that high absolute propensity to search |∂L/∂S| corresponds to high level of
consumption. It happens, because high absolute propensity to search increases the time of search.
Additional search results in low price and in additional non-labor income. And additional non-
labor income increases consumption.
But when increase in absolute propensity to search raises level of consumption, it decreases at
once the leisure time. From (3) we see that high absolute propensity to search corresponds to
short leisure time. And we can state that increase in absolute propensity to search raises the
intensity of consumption Q/H. (Fig.3).
Fig.3
Consequently, the model highlights the correspondence between physical ability to consume,
both labor and non-labor income, and consumption itself. In reality, “individual with different
abilities will make different choices of (C,Y) pairs, since they have different indifference curves.”
(Stiglitz, J.(1982, p.218)).
7
We can use this illustration as graphical interpretation of consumers' behavior in supermarkets
and convenient stores. Individuals with high intensity of consumption visit supermarkets, while
convenient store seems to be a right place for individuals with low intensity of consumption.
A consumer chooses local market with certain price level and corresponding price dispersion in
accordance with his habitual intensity of consumption Qh/Hh. And he begins to search
appropriate price for a chosen item. His individual propensity to search ∂L/∂S adjusts habitual
intensity of consumption Qh/Hh to price reduction ∂P/∂S. And he chooses the intensity of
consumption Q0/H0, which corresponds a) to equality of marginal values of search; b) to
maximum of reserve for future purchases, and, c) to maximum of consumption – leisure utility U
(Q,H) on a particular market with given price dispersion.
4. Relative sufficiency in consumption
We can ask ourselves why consumers usually don’t exhaust all potential non-labor income
produced by price dispersion.2 The motive to create reserve for purchases seems to be a
necessary but not a sufficient condition to limit search activity and to accept high prices.
Effectively, if we come back to Fig.1, we can see that increase in consumption makes
expenditure curve QP(S) steeper and we find ourselves in situation when:
.S
PQ
S
Lw
So, in order to match marginal values of the key equation of the reserve maximization model (1)
we should continue search, now with increased absolute propensity to search |∂L/∂S|.
Let’s imagine an individual who has already maximized reserve for future purchases in
convenient store. What happens if he decides to increase consumption and to go to supermarket,
where prices are lower?
It is easy to demonstrate, that for a consumer, who has already maximized both reserve for future
purchases and current consumption – leisure utility at given level of price reduction, the search
2 Here we leave the problem of costs of searches measured by wage rate beyond the scope of this paper. The key
equation of the model (1) demonstrates the role of wage rate as one of limits of search activity. But the model can
also show how wage rate effects, with respect to income elasticity of demand, can produce interesting interpretations
of well-known phenomena of individual labor supply, like women’s higher willingness to substitute leisure for labor
and also like an “irrational shirking” in underdeveloped economies. But all these effects, described in related
literature, need more detailed analysis. That is why, this paper considers wage rate to be a constant value.
8
for new equilibrium is not so interesting. If he goes from high prices of convenient store to low
prices of supermarket, he increases consumption but he certainly decreases leisure time. And, as
result, he can decrease utility level (Fig.4):
Fig.4
An intuitive argument that the decrease of utility level happens when consumption and leisure
are complements, can be illustrated by fairly simple mathematical analysis.
Let’s analyze the changes in utility with respect to changes in price reduction. If we take for
illustrative purposes the absolute value of price reduction |∂P/∂S| as an attribute of a local
market, we have:
9
)10(0)|)(|
|)(|(0
||
|))(||),(|(
.0;0|)(|
|)(|;0;0
||
);|)(|
|)(|(
||||
|))(||),(|(
);
||
||(
||||
|))(||),(|(
);||||
(||
|))(||),(|(
);||||
(|||))(||),(|(
)(
/
/
/
//
)(
/
/
/
)(
/
/
//
//
)(
/
/
//
//
)(
///
//
//
///
QforH
SP
SP
SP
SPSP
QforH
SP
SPQ
SP
QforH
SP
SPQ
SPSP
SPSP
QforH
SP
SPQ
SPSP
SPSP
QforH
SPSP
Q
SP
SPSP
SP
H
SP
QSPSPSP
MRSdH
dQwhen
d
HQdU
MRSdH
dQMU
H
whereMRSdH
dQMU
H
d
HQdU
MRSH
Q
MUH
d
HQdU
MRSHQ
MUd
HQdU
HMU
QMUdHQdU
A transfer to another local market with low absolute price reduction certainly decreases leisure
time. So, in order to increase utility level, a consumer should compensate the loss of leisure
time by extra consumption.
We can see that changes in utility level depend on changes in consumption path dQ|∂P/∂S|/dH|∂P/∂S
with respect to the marginal rate of substitution of leisure for consumption at given utility level.
The value dQ|∂P/∂S|/dH|∂P/∂S exposes a shift from one optimal search decision to another, this time
with increased consumption and decreased reserve for future purchases.
(It seems that, when we find a new market with low price dispersion, we can easily increase
consumption and we can compensate the loss of leisure time. But it is not so easy, because we
are limited by marginal costs of search. The value w×∂L/∂S determines how much we can buy
at new level of price reduction ∂P/∂S. Indeed, if we decide to buy more and more at a new level
of price reduction, we cannot equalize marginal costs of search with its marginal benefit and we
cannot maximize reserve for future purchases.)
The following graphical interpretation of the set of equations (10) facilitates the understanding of
possible outcomes of decision to move to another local market with low absolute price reduction
(Fig.5):
Fig.5
10
An individual starts from point E0 where he maximizes both reserve for future purchases and
consumption – leisure utility. If his preferences result in the flat indifference curve Us0 he goes
voluntarily to another local market because there, at point E1s, he increases utility level from Us0
to Us1. It happens because
)11(0||
|))(||),(|(0)
|)(|
|)(|(
/
//)(
/
/
SP
SPSPQforH
SP
SP
d
HQdUMRS
dH
dQ
or increase in consumption overweighs decrease in leisure time, and the fall in absolute value of
price reduction increases the utility level.
But if his preferences produce the nearly L-shaped indifference curve Uc0, the consumption
pattern (Q1;H1) at point E1s is not interesting to him, because it corresponds to lower utility level
Uc1 with regard to initial utility level Uc0. So,
)12(0||
|))(||),(|(0)
|)(|
|)(|(
/
//)(
/
/
SP
SPSPQforH
SP
SP
d
HQdUMRS
dH
dQ
or shift to lower absolute value of price reduction decreases utility level. It happens because
increase in consumption doesn’t compensate decrease in leisure time. The absolute value of
substitution rate dQ|∂P/∂S|/dH|∂P/∂S, produced by shift from (Q0;H0) to (Q1;H1), is less than
marginal rate of substitution of leisure for consumption of initial utility curve Uc0. So, our
consumer doesn’t want to decrease utility level and go from Uc0 to Uc1. (If he has occasionally
met another local market before, he would find there a new equilibrium Ec1. But now this
equilibrium is unachievable, because he cannot “come back” and increase leisure time.)
We know that L-shaped indifference curves imply fairly small substitution effects, while flat
indifference curves explicit large substitution effects.
11
So, we can presuppose, that when utility is already maximized on a local market at given level of
price reduction ∂P0/∂S0, additional search for extra non-labor income and extra consumption on
another local market with lower price reduction ∂P1/∂S1 can increase utility level, only when
consumption and leisure are strong substitutes. When consumption and leisure are strong
complements, additional search decreases utility level.
And here we would like to apply to the results of the analysis of household labor supplies and
commodity demands, presented once by R.Blundell and I.Walker:
“Services and transport are strong substitutes for male leisure, whereas clothing, food, energy
and our definition of durables tend to be complements to male leisure. As might be expected
these goods do not necessarily have the same relationships with female leisure. Services tend to
be complementary to female leisure, clothing is a substitute and energy tends to be a
compliment.”3
From the point of view of the reserve maximization model, men are not satiable when they
search for services and they are ready to accept new equilibrium of marginal values of search at
lower price dispersion, whereas women are not satiable when they search for clothing items.
Nevertheless, the set of equations (10) shows us, that once search for additional service or for
new jacket can also decrease utility level.
We can see that additional search can create overconsumption effect, produced by diseconomy
on scale, this time by diseconomy on scale of search. That is why individuals don’t exhaust all
potential non-labor income, created by price dispersion and they choose a sufficient level of
consumption for both complements and substitutes.
The set of equations (10) emphasizes the regulatory role of the concept of marginal rate of
substitution as measure of relative satiation, this time with regard to price dispersion. In fact,
sufficient level of consumption is based on relative satiation, which can be described by marginal
rate of substitution of leisure for consumption. We can see that MRS (H for Q) limits search
activity. If we apply this conclusion to price-taking behavior, we can state that MRS (H for Q)
makes high prices more attractive and/or more acceptable.
So, we can make the logical interpretation of the set of equations (10) and of the graphical
illustration (Fig.5):
3 Blundell, R., Walker, I. (1982) “Modelling the Joint Determination of Household Labor Supplies and Commodity
Demands.” Economic Journal, 92, pp.351-364.
12
Individual ends up the search for lower price when he maximizes both reserve for future
purchases and current consumption – leisure utility, whereas an absolute value of expected
substitution rate dQ|∂P/∂S|/d H|∂P/∂S| of additional search equals to current MRS (H for Q).
If individuals always follow this rule, we never meet an overconsumption effect. But this effect
really exists. The model can explain overconsumption effect as well as effect of impatience,
because the marginal rate of substitution of leisure for consumption depends not only on prices
and wage rate, but also on explicit time horizon of consumption – leisure choice.
5. Time Horizon and Reasons for Impatience
When we take into consideration time horizon of consumption – leisure choice, we can see that
changes in wage rate and time horizon itself are not usually proportional. The simplest example
is the shift from daily wage rate to weekly consumption pattern. Week-end decreases the value
of habitual daily MRS (H for Q). And in order to restore his habitual MRS (H for Q) and to
compensate the deficit of labor income, an individual should search for additional non-labor
income, i.e., to search for more interesting local market with lower price level. And if he finds it
and if there he really restores his individual MRS (H for Q), then:
)13(168
1
/168
1
/24
1
/)(
11
5
00
7
00
1
SP
w
SP
w
SP
wHforQMRS
daysdaysday
When an individual plans his weekly consumption pattern on the base on daily wage rate, he
inevitably comes from daily equilibrium Ed not to the equilibrium E0w, but to the disequilibrium
D0w, which corresponds to weekly allocation of time between labor, leisure, and search (Fig.6):
Fig.6
13
But the disequilibrium point D0w lies below his habitual consumption path. And, what is more
important, the MRS (H for Q) at this point is less than MRS (H for Q) at his daily equilibrium Ed.
According to the set of equations (10), the lower value of MRS gives him a chance to search
more. So, he should try to restore his consumption path as well as his MRS (H for Q). Saturday
morning he definitely cuts his leisure time from H0w to H1w and he goes to supermarket. And if
he really restores there his individual MRS (H for Q), he automatically increases consumption
well above equilibrium level E0w. He finds himself at new equilibrium E1w at utility level U1w.
When increase in time horizon decreases the expected value w×∂2L/∂S∂H, a need to compensate
expected loss in labor income stimulates search for additional non-labor income and for lower
absolute value of price reduction |∂P/∂S|. There are many factors that can produce the same
effect. Here we can pay attention to risk, uncertainty, interest rate, and product lifecycle4. All
these factors can create the effect of overconsumption. For example, uncertainty decreases
expected wage rate with respect to certain time horizon. Following the equation (4), we can say
that uncertainty decreases expected MRS (H for Q). A consumer tries to compensate uncertain
labor income by non-labor income. But when he restores the MRS (H for Q) in a manner,
presented at Fig.6, he inevitably increases consumption well above his habitual consumption
path. So why, “the MPC for a consumer facing uncertainty is strictly greater than the MPC for
the corresponding perfect foresight consumer.” (Caroll, C.D.2004 p.16).
When we try to compensate actual or expected loss of labor income by non-labor income and to
restore the MRS (H for Q), we inevitably increase our intensity of consumption. If we re-arrange
the equations (4) and (5) we can expose the correspondence between intensity of consumption
Q/H and MRC (H for Q) in a following form:
)14(//
//
)( ,/22
H
QHSL
SL
QHSL
SP
w
Н
QHforQMRS HSLe
Additional search increases absolute propensity to search and it decreases leisure time. But the
equation (7) shows us, that these changes result in decrease of elasticity of propensity to search
with respect to leisure time. And if we try to restore the MRS (H for Q), we should increase our
intensity of consumption.
4 The analysis of intertemporal decision-making, based on interest rate, goes beyond the scope of this paper. Here
we can only pay attention to the fact that MRS(H for Q) ratio consists of three variables, which are time dependent.
The fairly simple mathematical logic says that we cannot eliminate factor of time from MRS (H for Q) ratio. So,
MRS (H for Q) is also a time dependent variable. This consideration becomes crucial, when we take into
consideration product lifecycle, i.e., lifecycle of durables or big-ticket items.
14
6. Neoclassical Paradigm, Search-Satisficing Concept, and Easterlin Paradox
The explicit nature of time horizon of consumption – leisure choice accentuates the role of the
concept of marginal rate of substitution of leisure for consumption and it gives a chance to
review the historical discussion between Chicago school and H.Simon’s search – satisficing
concept as well as to reconsider modern concepts of relativity of utility, largely based on so-
called “Easterlin paradox”.
When we take time horizon as constant value, we can see that individuals with different abilities
to consume have different search tactics. They choose different sufficient levels of consumption,
which correspond to different indifference curves. But if we take time horizon as variable value,
we can theoretically construct an indifference curve, which joins individuals with different wage
rates and different propensities to search, who make purchases on different local markets (Fig.7):
Fig.7
Indeed, the development of the reserve maximization model can contribute to the analysis of the
problem of relativity of utility. But this way seems to be methodologically very long because it
first of all needs the willpower to understand the relative nature of utility itself.
In this sense the discussion with procedural approach and search – satisficing concept seems to
be much shorter. H.Simon wrote once:
“In an optimizing model, the correct point of termination is found by equating the marginal cost
of search with the (expected) marginal improvement in the set of alternatives. In a satisficing
15
model, search terminates when the best offer exceeds an aspiration level that itself adjusts
gradually to the value of the offers received so far.” (Simon, H. (1978, p.10)).
The reserve maximization model redirects our attention from marginal values of search to the
value of MRS (H for Q). The equalization of marginal values in decision-making process
becomes a problem of secondary importance. Taken as constraints to the utility maximization
problem, marginal values of search give up the focal point in decision-making to the concept
of marginal rate of substitution as to the resolution of this problem.
In fact, from the monetary point of view the optimal search corresponds to the equality of
marginal values of search:
)1(S
Lw
S
PQ
But from psychological point of view the optimal search represents a choice of certain level of
price reduction, which corresponds, at given wage and time horizon, to physical trade-off
between consumption and leisure:
)15()(/
1|)/( 2 HforQMRS
H
Q
SPHSLw
iiconst
In reality, consumers don’t calculate marginal costs and marginal benefit of search. They could
be limited only by a common feeling, that search is certainly a loss of valuable time of labor as
well as of loved time of leisure. And they simply choose a particular niche in price dispersion in
order to get satisficing or optimal combination of consumption and leisure. This satisficing level
should correspond to their MRS (H for Q), because in other way they feel frustrated.
The gradual adjustment of aspiration level happens because, in reality, price reduction is neither
monotone, nor continuous, and expected wage rate and time horizon are not constant in
psychological sense.
We can presuppose that for any satisficing decision we can find a particular set or combination
of expected values of wage rate, price dispersion, and time horizon, which correspond to a
certain maximum of utility of consumption – leisure choice. So, we can see that a model of
satisficing behavior doesn’t need advanced psychological studies and it can be easily described
by fairly simple economic tools.
16
However, we should not reject the concept of procedural rationality at all. For example, decision-
making process, described by the reserve maximization model, can be easily interpreted by the
prospect theory.
7. From “Common Model” of Behavior to “Leisure Model” of Behavior
If we come back to ∂L/∂S+∂H/∂S+1 =0 rule, we can see how a consumer can really “come
back” to attractive local market and increase both search and leisure time. In fact, when ∂L/∂S>-
1⇒ ∂H/∂S<0. But when ∂L/∂S<-1⇒ ∂H/∂S>0. (Fig.8)
Fig.8
The value ∂L/∂S<-1 is produced by our willingness to cut definitely labor time in order to
increase both search and leisure. And this value becomes a real problem for consumption –
leisure choice, because it transforms consumption into “economic bad”.
We can see that when ∂L/∂S<-1 ⇒ ∂2L/∂S∂H<0. But when the value ∂
2L/∂S∂H becomes
negative, the equation (5) gives us positive value ∂Q/∂H. Budget constraint changes its slope and
indifference curve changes its shape (Fig.9). It happens, when T = L(S) + H(S) +Hmin +S, and
aspiration or minimum level of consumption is unattainable because an individual is forced to
give up physical and/or psychological minimum of leisure time Hmin.
Fig.9
17
This model of behavior can be described as “luxury model”(∂L/∂S<-1⇒ ∂H/∂S>0) in
comparison with “common model” of behavior (∂L/∂S>-1⇒ ∂H/∂S<0), presented by Fig.2. We
can find examples of “luxury model” of behavior not only in high societies of developed
economies, but also in rural societies of underdeveloped economies.
8. Veblen effect
The most interesting attribute of “luxury model” is the rationalization of Veblen effect. We can
see that Veblen effect is rational for “luxury model” of behavior (Fig.10):
Fig.10
When price growth stimulates search, the relationship between price and time of search becomes
positive (∂S/∂P>0). Let’s imagine a Hollywood star who begins to search at new price level. If
she increases search time, she automatically increases her leisure time (∂H/∂S>0). In order to
18
“load” this additional leisure she increases consumption (∂Q/∂H>0). As a result, a price growth,
followed by increase in leisure as well as in consumption, raises the utility level (∂Q/∂P>0;
U1>U0). A Hollywood star can really feel satisfied when she increases her consumption at a new
price level. Indeed, conspicuous consumption and conspicuous leisure complements each other.
9. Protestant Work Ethics
Coming back to the “normal” model of behavior, we could find an example contrasting with
Veblen effect, when individual decreases consumption in order to avoid ostentation5. The
counter Veblen effect guides the analysis of the reserve maximization model to an important
conclusion. If we interpret low absolute propensity to search as manifestation of high
willingness to work, the key equation (1) of the reserve maximization model tells us, that low
absolute propensity to search corresponds to low level of consumption
If we convert the key equation of the model (1) into elasticity form, we get:
)16(,
,
sp
sl
wL
PQ
S
PQ
S
Lw
ee
We can see that for a given relative price reduction spe , relative propensity to search sle ,
corresponds to average propensity to consume.
So, the equation (16) represents the algebraic illustration of major attributes of protestant ethics –
hard work, propensity to save, and modesty in consumption. The reserve maximization model
transforms these considerations into the following form – low relative propensity to search
corresponds to low average propensity to consume (Malakhov, S. (2003).
Conclusion
The model presented in this paper bypasses both concept of costs of search and concept of costs
of leisure. It represents an attempt to describe consumers’ behavior by monetary values of labor
income and expenditures. Concepts of propensity to search and of price reduction, taken as
derivatives, cannot be used directly as appropriate costs’ measures. But such an escape from cost
5 Lea S.E.G., R.M. Tarpy and P.Webley. (1987). “The Individual in the Economy: a survey of economic
psychology”. Cambridge: Cambridge University Press, p.205
19
analysis to monetary analysis doesn’t seem methodologically inconsistent. Moreover, it gives us
an additional “degree of freedom” when we proceed to the analysis of utility maximization
choice.
The model presented here induces many interesting reflections in different fields of economic
science. Here we would like to pay a particular attention to the two of them. The first is the
correspondence between search and home production. If we attempt to develop the basic
approach to allocation of time, proposed by G.Becker (1965), we can describe some home
activities in a form of QP(S) function, where search for lower price corresponds to “production
of useful commodities”, for example, to cooking.
The second is the problem of measurement. We think that the absolute propensity to search, key
parameter of the model, can be deducted from average propensities to consume and from data on
price dispersion, which economists have successfully investigated. But inducted field studies of
propensities to search, in correspondence with particular consumption, patterns seem to be more
interesting and more promising.
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