KEO Discussion Paper No. 132

Priority Order and Consumer Behavior*
Fumimasa Hamada
May 2014

Abstract
This paper attempts to propose an alternative microeconomic theory of consumer
behavior in terms of distributional approach.

A model determining the optimalpriority order of and demand for consumer goods not only of the homogeneous type but
also of the heterogeneous type under the budget constraint of a consumer and themarket conditions is presented. Utility of a commodity is decomposed into the value in
use and the value in quality. The latter is assumed to depend on personal income level.
Market demand for each commodity is also determined.

Key Words: Heterogeneous commodity, utility maximization, optimal preference order,
income distribution, consumer demand.

JEL: D01, D03, D11, D31.

* The author thanks Shinsuke Nakamura, Michitaka Hikari, Toru Maruyama and Masao Fukuoka of

Keio University for their helpful comments and discussions. He is also thankful to Masao Ogaki of
Keio University and Mamoru Kaneko of University of Tsukuba and other participants for comments at
the Keio Seminar and at the Joint Meeting of Mathematical Economics Monday Seminar in Keio
University. The author is Professor Emeritus, Department of Economics, Keio University, 2-15-45
Mita, Minatoku, Tokyo 108-8345, Japan. E-Mail: yamamine-75@pa2.so-net.ne.jp

11. Consumer’s Utility: Quality and Ordering of Choice
The traditional theory assumes, in general, that any consumer goods has a smoothdeclining curve of its marginal utility, but this assumption is not able to be applicable tomany consumer goods, because in reality, there are three types of commodities; that is,
type A is of the commodity like as treated in the standard text book, the marginal utility
curve of which is smoothly declining. Type B is of the case where the marginal utility
curve has a fairly steep down-slope, and type C is the case where the marginal utility
curve is vertical that means that marginal utility of the second unit is equal to zero.
Many kinds of clothes, shoes, cups, plates, and other daily consumption goods and so on
could be considered to be of type C. Consumer’s decision to purchase this type ofcommodity is just to buy or not to buy it in most cases. In case where the consumption
bundle includes commodity of type C in the ratio not to be negligible, it may hardly bepossible to assume that there are smooth indifference curves on the super space of themulti-dimension by number of commodities available like in the neoclassicalmicroeconomic theory of consumer behavior. In order to extend microeconomic theoryof consumer behavior towards the more realistic, consumer’s preference among
consumption goods has to include the extreme case like as of type C described above.
Though we accept, in part, the law of decreasing marginal utility, we also take into
account of the case where marginal utility curve has a vertical slope, so we assume that
consumer decides the priority order of consumption goods to buy so as to maximize total
utility of the consumption basket with the budget constraint subject to each personal
income and the market conditions as given.
Let us assume that utility value of any consumer goods can be divided into two
components; appreciation of necessity or usefulness, and quality. The former is thevalue in use or a basic utility of consumer goods for human life. When a consumer
makes decision to purchase any commodity, this consumer is assumed to decide apriori
the priority order of purchasing. This a priori order may depend not only on its value
in use in daily life, on one hand, but also on its attractiveness, in other words, on theappreciation of its quality on the other hand.
Now, let us define utility of one unit of a commodity divided by its price as the unit
utility. This is the utility of one unit of a commodity per unit currency, say, Yen. The
price of commodity is important, so more exactly, the a priori preference or priority
order of that commodity could be assumed to be determined by the volume of unit utilityof that commodity. Here it should be noted that the quality of each commodity is given
an important role. The difference of quality of each commodity is the core point in themodern economy when the income differentials are prevailing. In the present society,2consumer seems to be interested in diversity of consumption, so that it may prefer thecommodity of different quality, instead of increasing quantity of the same commodity.
Let us think about the reason why consumer makes decision of purchasing acommodity among others. It may be realistic to assume that consumer selects thecommodity of the highest unit utility among the commodities first. For example, there
are many sorts of meat of different quality within the meat item. We have to makeclear of the reason why a sort of meat of some quality is selected among others by aconsumer. In order to think about this, it may be necessary to define the utility value
in more detail.
2. Priority Order of Purchasing: Utility value theory of purchasing power
Utility value of consumer goods is defined as the subjective value of it. However,this is not what is declared by consumer’s words but is what is expressed through its
behavior of choosing and consequently purchasing it. The value of a commodity can beconsidered to be established by a consumer to choose and purchase it in its market. We
also accept that the traditional or neoclassical theory of consumer behavior assumes
that utility value of a consumer goods is given by one’s subjectivity.
So, there is assumed to be the same number of preference function as that ofconsumer. There may be a tacit understanding that it includes value in use andattractiveness; that is, the former is the usefulness or the necessity for daily life and thelatter is appreciation of a sort of additional value to utility value such as quality, design,color, feeling, fashion and so forth.
Let us call this as the value in attractiveness from now on. Value in use of acommodity may also be subjective, and for the simplicity’s sake, let us assume that theutility of consumer is equal to the sum of the utility over all goods which consumerpurchases. In other words, utility of one unit of a commodity is independent of that ofother commodities 1.
Value in use of consumer goods is a part of utility of one unit of a commodity, and it
can also be assumed to decline, as the unit to purchase increases. In this implication,
value in use is assumed to be subject to the law of decreasing marginal utility. As
already noted, there may be three types of commodity, classified in terms of the shape of
marginal utility curve: type A, type B and type C. Utility of the last one unit of acommodity turns out to be smaller than that of the previous order in the case ofcommodity of type A and type B.
1

It may be possible to extend this extremely restricted case to more general case, but this may be thenext stage of this study.

3

Value in attractiveness of a commodity is also subjective, but this can be thought
as considerably influenced by income of each consumer. For example, a consumer oflower income, when to make decision of choosing and buying rice, will not attach any
greater importance to the value in attractiveness of any high quality of rice because of
its severe budget constraint. In other words, value in attractiveness as an importantcomponent of utility of consumer goods depends on the excess capacity of the purchasing
power of each consumer. Because of the budget constraint, consumer of lower income
has to discount the value in quality of each consumer goods, though it is recognized as apart of utility value. It should also be noted that producer of commodity may insist theattractiveness of each commodity by advertizing, so consumer is assumed to appreciate
or depreciate that based on its purchasing power; that is, its income level.
Since the value in use of a commodity is not common to all consumers, its utility
value as the sum of value in use and value in attractiveness is finally determined by thevalue in use and the income level of each consumer. Consequently, utility value of one
unit of a commodity as the subjective value of consumer goods is determined by the two
objective factors: the quantity of consumption and the income level of consumer with thestructural parameters including the personal attributes of live-style specific to eachconsumer as given. More exactly, the value in use is a decreasing function of thequantity of consumption, and the value in attractiveness is an increasing function of
personal income level. 2

Thus, for instance, even within one consumption item,

consumer could be assumed to select a commodity based on the order, from the higher tothe lower, of the unit utility of commodity described above, and here, income level ofeach consumer takes the most important role in deciding the order of selection.
It may be possible that even within one item, consumer selects a commodity of thehighest unit utility defined above and also may select the second and the third, and so
on with its income level as given. But the second and/or the lower selection within an
item may not necessarily be the case of consumer of the higher income. There may be
the other commodity of the higher unit utility in other items to this consumer. So, aconsumer will select one commodity within each consumption item, and will decide theoptimal priority order of all the commodities available in the market from thecommodity of the higher unit utility; that is from the highest unit utility through thelowest under the budget constraint. This implies that consumer is assumed to maximize
total sum of utility per one unit of currency and consequently by multiplying the sum of2

A special case will be used, to explain the role of individual income when the optimal priority order isdetermined as shown in Table 1. However, in the theoretical model to be presented in the later section,
value in use is assumed to be completely subjective of each consumer.

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budget to it, the total utility of this consumer. Since the unit utility of commodity oftype A or type B is a decreasing function of the quantity of its consumption, there could
be included some units of the same commodity to be selected as that of different priority
order from others.
From the view point of the utility value theory defined as above, the samecommodity is not the same to each consumer who has a different income. This can beshown by an example of a special case where there are two commodities of different
quality but of the same value in use within a consumption item.
Let us define V k i (qi ) , (i = a and b ) as the value in use of one unit of commodity iof consumer k, and W k i (yk ) as the utility of attractiveness of one unit of commoditythat consumer k with income yk purchases after (q i -1)units is to purchase,q i =1,2,・・・,Q i ; and U k i as the utility of one unit of commodity i, so that,U k i (qi , yk ) = V k i (qi ) + W k i (yk − 𝑦𝑦�) , y� = {∑K
k=1 yk }/K

Vik ≥ 0 , Wik > 0, i = a,b, k=1,2,・・・,K, q i = 1,2,・・・,Q i

Suppose that there are two consumers (K=2) whose income is different; that is theincome of consumer 2, y 2 is higher than that of consumer 1, y 1 . In Table 1, Vik , utility

value in use of one unit of commodity a and b is supposed to be the same to consumer 1

and 2; that is 100. Utility value in attractiveness of commodity a, Wa is 80, but that ofcommodity b, Wb is 300, and these values can be assumed to be a sort of the firm’s side

evaluation. So utility of one unit of commodity a, Ua and that of b, Ub is 180 and 400

respectively. Suppose that consumer 1 evaluates the attractiveness of commodity a,
Wa1 as 20, and that of commodity b, Wb1 as 30 subjectively, depending on the income

level of consumer 1 that is assumed to be lower than that of consumer 2. Then consumer

2 is assumed to evaluate subjectively the attractiveness of commodity a, Wa2 as 80, andthat of commodity b, Wb2 as 300 based on its higher income.

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Table 1 The Choice of Commodity within an Item – An Illustrative Case
Commodityab

Value in use

V

100

100

Value in attractiveness

W

80

300

Utility

U

180

400

Value in attractiveness of consumer 1

W1

20

30

Value in attractiveness of consumer 2

W2

80

300

Utility of consumer 1

U1

120

130

Utility of consumer 2

U2

180

400

Price of commodity

P

10

20

Unit utility of consumer 1

Ω1i

12

6.5

18

20

Yes

No

No

Yes

Unit utility of consumer 2Ω2i

Choice of consumer 1
Choice of consumer 2
Note: All variables are in terms of one unit of commodity.

Thus, utility of one unit of commodities a and b of consumer 1 are 120 and 130, as
denoted by Ua1 and Ub1 respectively, but, of consumer 2, they are 180 as Ua2 and 400 asUb2, depending on the higher income. Suppose that the price of commodity a is 10 andthat of b is 20. Then, the unit utility of commodity a and b of consumer 1, Ω1a and Ω1b is

12 and 6.5, but that of consumer 2, Ω2a and Ω2b is 18 and 20 respectively, andconsequently, consumer 1 decides to purchase commodity a, but consumer 2 decides topurchase commodity b that is assumed to have the higher quality or attractiveness. It

may be realistic to assume that consumer who decides to purchase commodity like bdoes not purchase commodity like a. The same is true for the case where there are
more than two commodities within a consumption item.
3. Purchasing Power of Consumer and Demand for Consumer Goods
Purchasing power of each consumer mainly depends on the income and the rate ofsaving. There can be considered many factors to influence on the saving rate of income.
Economic theory has so far developed the mechanism that many factors change the rateof saving of consumer income. Though each theoretical mechanism has been madeclear in some degree, it is still not clear how the rate of saving is determined by thosefactors as a whole. Keynes has finally proposed to accept a standard value by theempirical law of propensity to save. This may be a sort of the standard value of “g” (=9.806m/s 2).
6

Following Keynes, consumer knows that there are many factors influencing thetime preference of consumption with the income level as given, but its whole mechanism
appears too complex to take into account, so that as a realistic solution, some rate ofsaving is accepted based on the past experience. As a consequence, the purchasing
power or the budget constraint of each consumer can be considered to depend on its
income level and the rate of saving or propensity to save.
Given income level and propensity to save of each consumer, the budget constraint
or purchasing power of each consumer is predetermined, and given the prices ofconsumer goods and the budget constraint of each consumer, demand for consumption
goods by each consumer can be determined by the priority order of consumer goods;
That is, the optimal priority order and the budget constraint gives rise to the maximum
utility to this consumer.

The unit utility of consumption goods depending on theincome level of each consumer decides the optimal priority order, from the highest
through the lowest, to purchase.

The budget constraint determines demand for

consumer goods, and the income distribution determines the market demand for
consumer goods and also the aggregate demand for consumer goods.
4. A Model of Priority Ordering and Demand for Consumer Goods
In order to make clear of the basic idea of this theory of priority order, let us
propose some basic assumptions as bellow:
Assumption 1
Utility of one unit of a commodity is decomposed into the two components; that is,the value in use and the value in quality. The former is the usual utility value, andthe latter is an increasing function of income of each consumer.

Consumerappreciates the value of a commodity not only for its usefulness, but also for its
attractiveness such as material quality, design, color and so on.
Assumption 2
Consumer maximizes total utility by making priority order of utility of one unit ofcommodity per unit of currency, from the highest through the lowest.
Assumption 3
There are three types of the curve of marginal utility or value in use; that is, type A,
type B and type C.

In type A, utility of additional one unit of commodity issmoothly decreasing as its consumption increases. In type B, utility of additional
one unit of commodity is drastically decreasing. In type C, utility of additional one
unit of commodity is equal to zero.
7

In Assumption 1, consumer durable goods could be dealt with so as to be consistent
with the usual non-durable goods; that is, the quantity of factor services in unit periodof durable goods is proportional to its stock. This assumption is just the same as thatin the theory of capital. Consumption of durable goods is its quantity of the factor
services in unit period. If the number of years of durability of that goods is T, and its
real value is C d , the consumption of that durable goods in unit period, say one year, isequal to C d /T. So, the real value C d is the real investment in it by this consumer.
Assumption 2 implies that utility of one unit of commodity divided by its price canbe recognized as utility of one unit of commodity per unit currency, say Yen, and let us
call this the unit utility. The unit utility of the same commodity may appear several
times in different priority order, and if the unit utility of two commodities is the same aseach other, the commodity number is made precedent in the priority order. The sum of
the unit utility of each commodity selected by the priority order gives rise to the
maximum value of the total unit utility under the budget constraint, so by multiplying
this sum with the sum of budget, the total utility is maximized.
Let us define the unit utility of commodity i of person k as Ωki , i=1,..,M; k=1,..,K.

Then,

Ωki ={Vk i (q i )+Wk i (𝑦𝑦𝑘𝑘 )}/p i =Uk i /p i , Vk i(q i ) ≥ 0, Wik (yk ) > 0,(1)

i=1,…,M and k=1,…,K,

where Vk i is the value in use and Wik is the value in attractiveness of commodity i toperson k who earns income y k , and p i is the price of commodity i.
Let us call W i k as the attract function; that is, the attract function can be specified
as below:𝐤𝐤𝒌𝒌
Wik (𝑦𝑦𝑘𝑘 ) = αki + βki (yk − 𝑦𝑦�) , ӯ = �∑K
k=1 yk �/K, αi , βi › 0,(2)

i=1,2,…,M, and k=1,…,K,

where αki and βki is constant respectively.
R

R

Then, the priority order of Ωki is;Ωk = {Ωki(1) , Ωki(2) ,.,Ωki(j) ,..,Ωki(M′) },𝑘𝑘𝑘𝑘
𝛺𝛺𝑖𝑖(𝑗𝑗)≧ 𝛺𝛺𝑖𝑖(𝑗𝑗+1), M’≥Mfor the income of person k, k=1,2,…,K,(3)

where Ωk is the set, the components of which are in the order of priority decided byperson k who gains income yk . The subscript i(j) implies that the commodity number ofthe commodity to be selected in the jth order is i. As already notified, if there are two

commodities the size of the unit utility is the same as each other, the commodity
number is made precedent in the priority order.
If Ωk i(j)=h =Ωk i(j)=h’ , then let us assign the priority order like as below:
Ωk i(j)=h ≷ Ωk i(j+1)=h’ subject to h≶h’.
8The relation between the budget constraint and income of person k will soon be
explained later.
Expression (3) also gives rise to the purchasing list of consumer goods under thebudget constraint of person k. Let us assume that the budget constraint of person k
who earns income yk is expressed as ck yk where ck is the average propensity toconsume of person k. Then, the optimal priority order of consumer’s goods of person k

can be determined by the inequality as below:∑O
j=1 pi(j)=h ≦ ck yk ,kk=1,…,K,(4)

where pi(j)=h is the price of commodity h of the jth priority order during the unit periodR( Ex. week, month, quarter, half year or year), so Ok is the number of the last priority
R

order, and y k is the income of person k, the distribution of which could be subject to thefunction of the Logarithmic-Normal type. It should be noted that the index j is not the
number specific to commodity, but the number of the priority order of commodity.
The priority order set of unit utility for all incomes K is defined as below:(5)

f: {y, p} → {𝛺𝛺1 , … , 𝛺𝛺𝑘𝑘 , … , 𝛺𝛺𝐾𝐾 } = Ω ∈Γ,y = {y1 , y2 , ・・・,y k , ・・・, y K }, p = {p 1 , p 2 , ・・・, p i ,・・・, p M }where Γ is a set of non-increasing finite series of non-negative real number. For eachorder set in Ω, the commodity identifier Ik is like as below:

Ik = {ik (j) = h} = {1 1 … 1 7 7 7 … 7 5 6 6 6 8 11 … },j=1,…,Ok(⋛M) 3, h=1,2,・・・,M,(6)

k=1,2,・・・,K,

where i k is the commodity number that is included in the optimal priority order of
selection by consumer k with income y k , and ik (j) = h implies that in the optimalpriority order decided by consumer k, the commodity number of the jth order is h. Ok isthe lowest priority order of consumer k. Since some commodity may be preferred morethan once in different order, Ok may turn out to be greater than M, the last commodity
number.
Now let us define Өk as the quantity identifier to make the optimal priority orderj correspond with the commodity number i and its quantity q i as below:kӨk = �∑O
j=1 q i(j)=h � = {15 0 0 0 1 3 12 1 0 0 1 … . } , k=1,…,K,k(7)

where qki(j)=h = 1, and qki(j)≠h = 0. Each number within the parenthesis is the quantity ofcommodity i (= 1,2,…,M).

3

With the values of pi , yk and ck as given, and using (7), the inequality (4) for

The number in the parenthesis is the original commodity number. There may be more than one unit
for some commodity to be selected as shown in (6), where there are 15 units of the commodity No.1 tobe selected.

9

consumer k determines the sum of consumption expenditures and its components to bepurchased under the optimal(utility maximizing) priority order of consumer goods.
∑M
i=1 Өik pi ≤ ck yk ,k=1,2,…,K(8)kkwhere Өik is the ith element of Өk , ∑O
j=1 q i(j)=h . The reason why this order of priority is

optimal is that this consumer can realize the maximum utility by deciding to select thisset of consumer goods under the budget constraint and the market conditions.

As the income level of consumer changes, the unit utility of commodity changes
through the change in the value in attractiveness, and so, the optimal priority orderchanges. Given the income of consumer and the market conditions, the corresponding
optimal priority order is determined, and consequently, the sum of consumer’s demandof each person with the optimal priority order is determined. That realizes the
maximum utility attainable by the person in question. Needless to say, the marginalutility of money of this person is equal to the utility of the commodity of the lowest
priority order.
Now, with the distribution of consumer’s income and the market conditions likeprices of consumer goods as given, the market demand for consumer goods isdetermined for each consumer. If the summation is taken with respect to the index k,
the equation for market demand for each commodity can be obtained as below:
Di = ∑K
k=1 Өik , i=1,2,…M,(9)

where M is the last commodity number in the market.
Needless to say,kO
Ө I = {∑K
k=1 ∑j=1 q i(j)=h } ={Ө i } = {D i }k(10)

i=1,2,・・・,M, h = 1,2,・・・,M.

Reviewing (5),whereg: Φ → ӨI ⊂ RI ,
Φ = Y 1 x….x Y K x P,

(11)
y 1 ϵ Y 1 ,…, y K ϵ Y K , {p i } ϵ P,

Where RI is the direct product set of Ith order.
5. A Social Change in the Value in Use

There have taken place some important social topics, such as metabolic syndrome,
the natural foods fashion, the ecological intention and so forth. These intentions will
give rise to a reduction of the value in use of a specific commodity that leads to adecrease of the unit utility of the commodity in question, so that its priority order drops
down in some degree or more. Because of that, this commodity might be removed out
from the consumer’s selection.
10

On the other hand, if this social change is what increases demand for any item,
like as in the change for the ecological goods; that is, demand for this commodity will
increase, and consumer will cut the purchase for some other commodities of the lowest
priority order.
6. Substitution, Complement and Income Effect
In this model, substitution between two commodities is explained as their change ofthe priority order, so if there takes place a drastic change in their relative prices, one of
the two will be dropped from the final consumption list, and the other will be introduced
into the list.

A commodity selected in some order, may accompany with anothercommodity as the complementary one in the next order. For example, tea or coffee would
accompany with sugar, and sugar may be accompanied with some other cooking foods
like as meat and/or vegetables. So, the same commodity will appear in the lower order,
several times as complementary goods.
Income effect on the commodity of type C is simple; that is, if income of consumer
increases, this increment will be paid for other commodity of the priority order following
the lowest priority order. A decline of price of any commodity will also increase demand
for any commodity of the priority order following the commodity lastly selected.
7. A Graphical Presentation
In order to make clear of the idea of this study, let us try to make a brief graphicalpresentation of the mechanism of this microeconomic theory of consumer behavior
presented in this paper. Figure 1-a shows that utility of one unit of commodity i of type
A to be purchased by consumer k with income y k in a unit period decreases as the unit
to purchase increases.

On the vertical axis is measured utility of one unit ofcommodity i to be purchased by consumer k in a unit period. On the horizontal axis ismeasured the units of that commodity in the same period. Figure 1-b shows that thedegree of decrease of utility of one unit of commodity i is rapid for the case of commodityof type B compared with that of type A. Figure 1-c shows the case for type C.
Figure 2 shows a down-wards step curve formed by the priority order ofcommodities with utility of one unit of each commodity to be purchased by consumer kwith income y k, divided by its price in the order from the highest through the lowest.
For example, the commodity number, (i(1)=h), may be 100, 2, 7, or 150.

Some

commodities may appear more than once, in different order. We can depict K Figures,
where K is the number of consumers.
Figure 3 shows the form of attract function. The person whose income level y k is11less than the average y� is assumed to discount the value in attractiveness of that
commodity.

Consumer whose income is higher than the average is assumed toappreciate the value in attractiveness. The attractiveness to be discounted orappreciated is supposed to be built up and announced in advertising by the firm thathas made that commodity.
Figure 4 explains the process of determination of the optimal priority order ofconsumer goods to purchase.

On the fourth quadrant of the figure, the personal

income distribution is depicted.

The real line curve shows the distribution beforechange, while the dotted line curve shows after the change. If income distribution istaken in terms of disposable income that is considered as subject to changes in tax
system, the form of income distribution may also change. The situation of the same
income in the distribution before the change and after the change is made clear.
The first quadrant of the upper part of the figure shows the same figure
configuration as that on the Figure 2. The curve L corresponds with the diagram in
the case where personal income is y l and the curve k corresponds with that of personal
income y k . On the 2nd quadrant of the Figure 4, the horizontal axis measures the sumof payments to be made to get the commodities from the order of the number 1 throughthe number jth. If the person of income y l selects commodities up to the number j l , thenit has to pay the sum of E l, and if the person of income y k selects commodities up to thenumber j k , then it has to pay the sum of E k. It should be noted that we implicitly
assumed here without the loss of generality that the average propensity to consume isunity; that is, c l =c k =1 for the simplicity’s sake.
8. Marginal Utility of Money
The optimal priority order of consumer goods of a person k is, as already observed,
determined by its income, and this implies that the marginal utility of money is equal tothe unit utility of the goods lastly selected by this person based on its budget constraint
with the prices of all the consumer goods as given. Since the priority order of the unit
utility of a grand mansion located near the center of capital or the famous resort area
may be much lower among the others, the marginal utility of super high income person
may be equal to it. It is needless to say that the attractiveness of the grand mansion
depends also on the income level of each person, and so the priority order of this goods ofthe lower income person is quite different from that of the higher income person.
9. Concluding Remarks
We have so far considered the microeconomic behavior of consumer demand,
12

specified quite differently compared with the neoclassical theory. It was assumed that
consumer maximizes the sum of utility of one unit of commodities available divided byits price under the budget constraint. Needless to say, by multiplying this sum with thebudget, consumer maximizes its total utility. Though here is assumed the independenceof utility of commodity to purchase available to consumer, the priority order of eachcommodity is determined by the order of utility of one unit of commodity per unit
currency from the highest through the lowest, and this makes an implicit relation
concerning utility of commodity in the order of priority. Of course, the substitution
between commodities is not directly taken into account, but it is introduced very
restricted, but in a realistic way. In this theory, commodity substitution is notunderstood as partial but complete.
The reason why we proposed a new idea on the explanation of consumer behavior interms of distributional approach, described above, is that we hardly accept the law of
decreasing marginal utility that is considered as applicable to all the consumer goods
evenly. It may be rather rare case where this law can be applicable. Each commodity is
regarded as the one within almost the same consumption item as each other, but theprice of each commodity is different from each other. Price is understood as the main
factor that shows quality differences embodied in each commodity. And so, in most cases,
the consumer’s decision may be to buy or not to buy a commodity. The neoclassicaltheory does not explain these cases; that is, of type C. Instead, it assumes that
commodities within each consumption item can be aggregated into the so-called“composite commodity”, and this assumption may be very useful from the view point of
the theoretical internal consistency, in order to formulate the whole system of thegeneral economic interdependence that includes both the consumer’s behaviors and the
producer’s behaviors. However, this consumer schedule does not take into account of
the case where consumer selects one commodity from a set of commodities, each ofwhich has different quality and so different price but regarded as of the same kind, or
included in one consumption item.
An alternative theory of microeconomic behavior of consumer could also propose asolution for the optimal demand for consumer goods that gives the optimal priority
ordering under the budget constraint of each consumer and market conditions, in termsof distributional approach. “Arrow-Debreu economy” assumes that all the commodities
are “divisible on the indifference curves. We should say this assumption an axiom, andwe cannot accept this axiom because of its unreality.
The new approach presented here seems to have one possibility to synthesize thetheory of market demand for commodity with that of financial securities concerning the13liquidity preference by [5] 4, and the Marshallian market supply behavior of commodity
by [3] 5. An attempt to make a rough sketch of the new system of economic analysis ispresented in [1] 6 .

They are all attempted by the “Distributional Approach”. The

implicit understanding of real economy by the Cambridge oral tradition and J.M.
Keynes is considered as to draw a whole system including consumer behavior, firm’s
investment behavior, financial investor’s behavior, and so on.

References[1]Hamada, F.,”An Economic Theory of Income Distribution,” Mimeo, 2011[2]Keynes, J.M., The General Theory of Employment, Interest and Money, 1936.
[3]Marshall, A., Principles of Economics, 9th edition with annotations by C.W. Guilbaud,
Vol.1, 1961 459-460[4]Obi, K.,Observation and Theory of Labor Supply by Houshold, Keio University Press.
1910.
[5]Tobin, J.,”Liquidity Preference as Behavior towards Risk,” Review of Economic

Studies, 25:65-86, 1958.
[6]一―――, (1955),”Multiple Probit Regression of Dichotomous Economic Variables,”Cowles Foundation Discussion Paper No.1, 1955.

4

The first part of Tobin’s paper proposes the relationship between the distribution (difference) ofopinion about the normal price of a security and its actual price to deduce the demand function formoney.
5 A. Marshall presented the market supply schedule for a commodity as a series of price of acommodity that corresponds with the supply of the commodity produced by each firm,that forms the
distribution of supply of goods by firm.
6
F. Hamada presented a theory of labor supply, where there is the distribution of the subjective view
(value) on the disutility of the same kind of labor among the applicants, while the utility of the wage toobtain is the same to all the applicants. The more elaborate study is presented in Obi[4].If thedisutility of labor of all the applicants is smaller than the utility of the wage, then the number of labor
supply is equal to that of labor of the labor force. The “Neoclassical Postulate” corresponds with thecase where this distribution converges to its average value.

14

Figure 1-a

Changes of Utility of One Unit of Commodity

UikType A
k=1,…, K1

qi units

2

Figure 1-b Changes of Utility of One Unit of Commodity
UikType Bk = 1,….,K

1

qi units

2

Figure 1-c Utility of One Unit of Commodity
UikType Ck = 1,…., K

qi = 11

15

Figure 2 The Priority Ordering of the Unit Utility of Commodity
Ωki(j)=habk = 1,…., K

c
e

f
d

1 2 3

g

h

4 5 6 7 8

p

m n

o

l

q

9 10 11 12 13 14

The Priority Order of Unit Utility of Commodity
Note: a,b,…,q are the commodity number.
Figure 3 The Form of the Attractant Function
Wik (yk ) = αki + βki (yk − 𝑦𝑦�) ≥ 0 , βki > 0
Wik (yk )k = 1,…., K

0

yk

y�

16

j

Figure 4 The Optimal Priority Order and
Demand for Consumer Goods
Ωki

L
M

K

� Өik pi
i=1

El

Ek

0

yl

yk

0

jk

f2(yl)jjl

f2(yk) f1(yk)f2(yl)
450 line
y

f1(y)

17

f2(y)

f(y)