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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