Optimization and Balance of National Economy Models

Copyright © IFAC Dynamic Mod~lling Warsaw. Poland. 1980

OPTIMIZATION AND BALANCE OF NATIONAL ECONOMY MODELS K. K. Val'tukh Institute of Economics and Industrial Engineenng, Siberian Department of the USSR Academy of Sciences, Novosibirsk, USSR'

Abstract. Two series of national economy models which have been used in the U~SR for estimations of national economy development hypotheses are presented in chort. A solution to the problem of utility function construction for optimizing national economy models is suggested and verified on the sta tistics of Federal Republic of Germany. Opt1mizing national economy model; balance of productive capacities; objective utility (consumption) function; law of mass consumer's behaviour; statistical verification of the theoretical models.

Key~words.

planning. The work at the system

Il~TRODUCTIOll

a whole began at the Institute

as

in 1961 on the base of ideas suggested by A.G.Aganbegian. According to his suggestion the high-aggregated (containing 20-30 industries) dynamic input-output model was to be inoluded into the system. Two main versions of the model have been elaborated. The primary one represents a strictly balance model (N.F.Shatilov was its major inventor). In short, this version includes a usual statio input-output model with addition of the description of reimbursement of fixed assets removal (in another possible case - of amortization); a restriction for the labour resources employed in national eoonomy; a special matrix determining the minimum of investment for every branch and technological type of investment; recurrent relations describ~g the growth of fixed assets; the special matrix (scale) of growth rates of production for nonproductive consumption destined for determination of the structure of the production, in accordance with which the balance solution to the model is found.

The given report presents a review of a work carried out during more than fifteen years by the team of researchers (since 1967 - in a special department of the Institute of Economics & Industrial Engineering). The detailed exposition of the results has been nublished in several books and papers (see References). ~vo series of balance and optimizing models of national economy have been worked out, checked in experiments and used in computations of the perspectives of the USSR economy development: models for preplanning examination of the hypotheses of national economy development; models for examination of such hypotheses di rectly when working out a plan. During several years some models are being delivered for direct use to the state Plan Committee of the USSR (Gosplan). The delivering of some other models to the Gosplan vvas begun only recently. At the same time we are intensively elaborating some new models.

Using the model,the first oomputations of the development of the USSR eoonomy were carried out for 1966-1910. Then the Institute used the model for several analyses of the problems of development of the USSR economy. These analyses were being oarried out on immediate directives of the Gosplan from 1966. At the same time we proceeded with our own investigations directed towards the further improve-

A SERIES OF INTERCONNECTED AGGREGATED MODELS OF NaTIONAL ECONOMY WITH EXOGENOUS TECHNOLOGICAL PROGRESS The work on the models was built right from the start as a constituent part of the studies carried out at the Institute for elaboration of a system of models for perspective 21

22

K. K. Val'tukh

ment of the model as well as towards the elaboration of various theoretioal and practioal problems with its help. At the end of sixties the seoond (for. mally optimizing) version of the model was elaborated (I.A.ltskovioh was its major inventor). The version has the follovdng distinctions from the first one: the equations of the distribution of labour resources are substituted with inequalities; the piece-linear oonsumption funotion is ohanged for objeotive function maximizing consumption in a given structure; a special condition for the ratio of the national inoome accumulation to the oonsumption fund is introduced. In seventies just the second version has been used in practical calculations. Being formally optirnizing one. the model includes no faotors of real variability of economic development, such as the diversity of the technological progress directions, plurality of the feasible paths of consumption growth as well as of the strategies of accumulation, etc. Certain approximation to the really optimal solution can be, of oourse, obtained with the help of multivariant estimates technique. However there exists the possibility to deal vdth the balance model in the same way. In 1966 some investigations on elaborating of substantially optimizing intersectoral models were started as well as on creation of models for optimization of the ohoioe among different variants of national economy development appearing by computation of the dynamic intersectoral balance (DIB) •

Firstly, it is the model optimizing the net production investment ( the share of net investment in national income). Its interdependence with dynamic intersectoral balance is shown and carried to the stage of concrete methods: that is to say, with the help of the optimizing model of net investment the choice can be made among different variants of national economy development obtained on DIB. A computer programme direotly uniting the model of DIB \vith that of optimization of net production investment was elaborated; in other words, these models are presented as a united optimizing intersectoral model of national economy. The optimizing model of net produotion investment rate was ohecked by use of appropriate indioes of the USSR eoonomy for more than 20 years. Thus we were able to explain the stability of this rate,to fore oast the

most effective trend of its development. Foreoasts of the alteration of optimal net investment rate for 1966-' 1968 and for 1971-1975 were realized. The forecasts proved their value wi th a high degree of preoision (although the trends obtained in these forecasts differed substantially from the planned ones: a gradual rise of the rate of net investment in fixed assets was foreoasted in oontrast with plan directives to its reduction). The methods of work vdth the model are elaborated and published. The oomputations have also been published. Secondly, an optimizing dynamic interaeotoral model vdth objective oonsumption function has been oreated using the teohnique of the indiffe renoe surfaces in a speoially elaborated form meeting, in our opinion, the laws of the consumption rise. One of the prinoipal features of this model is that the ohanges in the struoture of net final product are conneoted in it with the ohanges in the oonsumption level reached during the plan period, in particular, with the ohanges in the volume of aocumulated durable and semi-durable goods; these factors are not and apparently cannot be refleoted in computations where the relations of the growth rates of the produotion of various goods are Bet beforehand, simply or in dependenoe upon annual alterations of the general volume of production for nonproductive consumption (the latter in pieoe-linear function forming a special matrix in DIB). The first variant of the methods of obtaining specifio data for work with the model was elaborated and ohecked in experiments (determination of the level of full satiation of needs and of their minimal neoessary satiation; the quantity of acoumulated durable and semidurable goods; durability of these goods, etoJ. The methods of information ensuring and of perspeotive oaloulations are published. A method is also elaborated for isolated use of the objective function for computations of structural shifts in oonsumption. Special works have been published describing in detail the experienoe of the model applioation to foreoasting of the mass oonsumer behaviour in the USA. Computation results for the USSR were also published. The model as a whole allows to explain general struotural shifts in oonsumption of the USSR population and to oome closer to the determination of most effeotive shifts for a perspective of 5-10 years. Some non-trivial results have been obtained. For example, the neoessity of residential oonstruction increasing

National Economy Models

wi th the growth rate no less than of

population real income one has been shown. Apparently this model has to be oonsidered as a model for pre-planning elaboration of the general conoeption of national economy development for a perspective no more than 7-10 years just as the above considered models of the same aggregation level. The term depends first of all on the possibility of substantiation of coeffioients, alterations of which must be based on a ooncrete foreoast of teohnologieal progress. Seoondly, the problem of foreoast of the changes in full needs of the population is not yet elaborated. (The first steps in this direction are being made at present.) There also exists a necessity to differentiate the part of net final product satisfying the needs of population from that satisfying other nonproductive needs of the society (government, science and so on). The theory, on whioh the objective function is based, pertains only to the needs of population. The elaboration of special methods of foreoasting the other part of net final product is one of the next tasks of perfeotioning the optimizing dynamic interseotoral models. 1

A SERIES OF MODELS OF INTERSECTORAL BALANCE OF PRODUCTIVE CAPACITIES Since 1967 our team jointly with the Gosplan (Department of Composite National Economy Plan, Main Computing Centre and Institute of Economic Researches) is elaborating a model of intersectoral balance of productive capacities. At present practioal computations are carried out on the. first variants of the model, and these variants are being delivered to the Gosplan. The interseotoral balanoe of productive oapacities (IBPe) presents a certain step towards optimization of the input-output models. The simplest (static) variant differs from such models in so far as restriotions are introduoed for the oapaoities as to produot kinds (restriotions only for the group of the most important kinds are allowed). In this form the model allows to oheck the keeping in balance 1V.N.Pavlov, N.N.Seliverstova, L.M.Ruvinskaia took part in the work reviewed here; the oomputer programmes were made by M.N.Nild.tenko, A.V.Shoherbinskaia.

23

of planned putting the capaoities into operation as well as the influenoe of the fulfilment of planned putting the capacities into operation upon the rates and proportions of economy development. The first variant of the mo~el does not allow to determine directly the balanced plans of investment and of putting the oapacities into operation. It becomes possible when using the seoond variant of the IBPC, which additionally includes restrictions on investment resouroes and indices of investment expenditures for the creati on of the oapacities. The variant gives a possibility to carry out computations of investment distribution among big branohes and, more concretely, computations for determination of plans of putting oapacities into operation that would be directed to eliminate existing partial disproportions and to stave off their appearing in plan period. Unfortunately, the information available at present is not Bufficient for realization of the second variant of the IBPC in its complete form. The seoond variant of the model can be further developed under the condition that the coefficients of direot material and labour outlays would be dependent upon the investments directed towards the realization of technological progress. During last years a transition from strictly determined statements of optimum problems to stochastic ones takes plaoe. The system of interoonneotions in the national eoonomy expressed through the quantities set in the model is not simply definite, and therefore no optimal plan can be oonsidered as the only possible one. There exists a lot of such plans, everyone of whioh may be optimal, although with a different probability. There also exists a lot of such kinds of produotive oapacities, ~hich may prove to be a bottleneck, although with various probability. At present an experience of realization of the first and second variants of the model in stochastic statement is accumulated. 2

2E.B.Ershov (Moscow), B.L.Lavrovsky, V.M.Massakov have taken part in the work, described in the present section; the oomputer programmes were made by E.A.Satanova.

K. K. Val'tukh

24

THE THEORETICAL UTILITY FU11CTION

For the construction of the optimizing models of national economy as a whole it is necessary to deoide a wi1e circle of theoretical problems. OlLe of the most essential among them seems to be the problem of consumption goods utility measuring. The hypothesis of the form of utility f~Lction was offered by the author in 1969. Up to the present time a series of investigations fo~ factual examination of the fuction has been carried out. In the present report one of the statistical studies is described. The detailed theoretioal substantiation and desoription of the technique of utilit~ funotion applications is given in ~, 3, 4, 5]. In short, it is assumed that mass consumer under the given income and prices is seeking for the maximal value of the follovdng utility function: 1

TI{. j J L,Zoko) ° J J

D D=eQ ~ Z/ / eJ k

°

where D is satiety degree of the totality of personal needs of society members in goods and services (within the limits of the traditional level of consumption and the level of full satisfaction); Zj is similar degree of satisfaction of a particular perspective need j (j = 1~):

z. = (v.- v. min ) / (~ax _ ~n); J

J

J

J

J

v j is the consumed amount of goods and services \vhioh satisfy the need j (under a high level of aggregation - in monetary units of measurement, under disaggregative calculations in natural units); v = (v 1 , ••• , v ); ° n vj~n is the historically formed necessary minimum of pointed goods oonsumption; ~n = (~in _~x is the 1 , ••• , ~n) n ; ~full need in pointed goods; ~x = ( v max , ••• , v_-lIlax) n - ; k j is the exponent 1 eliminating the aggregation effeot on the results of funotion D estimations.

In treatment of the symbols it is supposed that there exists an approximate mutually simple correspondenoe between aggregates of goods and servioes j and different needs.

It has been proved that, under the given -ymin and -ymax, an optimal trajeotory ofioonsumption growth in exoess to vm n is induced by function D, the trajectory which is governed by the following law of oonsumption struoture:

Vj=Aj , qj~ / (qrZj' (qrqj ,) for every j ; here

)+vrn (2)

Aj , = (Vj,-Vj~n) / ~x ;

qj' = 1 _

vjtn / ~x

qj = 1 _ ~n / ~x Thus the formula (2) plaoes the level of every aggregate of goods consumption into the simple oorrespondence to the consumption of especially chosen one marked j'. It is shown by analysis of (2) that hypothetical utility function has some attributes which oan be tested empirioally. If they are oonfirmed in such a procedure, it means simultaneously, firstly, an empirical corroboration of the hypothesis, secondly, an explanation of the structural shifts in population consumption from the general law. The subtlest attribute, i.e. suoh one that is most probably to be infringed, consists in the non-negativity (under certain assumptions concerning the ~in/vWax. J' J" see below) of the second derivatives:

d2y. ----t~ 0 dV j

,

i. e. in the convey~ty

of the o~timal consumption growth trajectory (2). This convexity means geometrically that in the two-dimensional space of vectors v = (vo, v.,) J J the optimal curve (2) connecting the points ~in and ymax lies (excluding these points) below than the straight line connecting the same points. Such convexity has to take place under the oondition: vj~n/ ~ = (~in/v~9.A), ~d if for a certain J v~, llli~/vmai_ · 0' - vz:un/v~x J J' then the c~~e (21 andJthe mentioned straight line are to be indiscernible. If there is an aggregate 9f goods or seryices j such that ~7n / vf!l~x J . vmln/_~ax Vj ,then the curve (2) J ~s j to be concave.

mrr

<

It must be pointed that parameters ~n and ~ax are usually unknown when we prooess the statistics and conse-

25

National Economy Models

quently we o~ot exactly determine the ratios ~ I vj:'X and vT-n/vrx. But for the examinations of the correspondence between the real oonsumption growth curves and the properties of curves (2) it is necessary to know only which one of needs j and j ' is more satiated. Usually in our calculations the need in food is considered as j' one (in the pure form, if possible, i.e. excluding alcoholio beverages as well as tobaooo). Aa a rule the need in ;,g.~d is the most satiated one (i.e. j,n/vj~ = '" max( vT-n/vrx). Since that the oonj

vexity of the real ourves is usually to be expected. Statistically the oonvexity has to be realized on sufficiently long sections of the real trajeotory of oonsumption gro\vth and therefore we'll below determine it, first of all, considering the interval between two extreme points of the analysed series of statistical observations. But these points might be ohosen acoidentally and therefore the corroboration of the theoretical law depends on a specific oharaoteristic of the real trajeotory - the monotony of its oonvexity. An heuristic technique for monotony testing will be suggested below. The corroboration of the hypothesis means that the ratios t A t V j _ v~-1 ,] U v. t t-1 = are growing wi th v j '- v j ' vj ' v j ' enlargement (here t is the index of statistical observations). If function D is the adequate reflection of a real law, then not only growth of ratios vj/v j ' but growth of ratios ~Vj/~j' has to observed on sufficiently wide intervals of oonsumption development. In substantial terms it means that structural changes in mentioned sense of word must have a tendency to be stronger and stronger. Thus no\O~Y_~el's t:rne laws (i.e. the stab e ren s of struotural ch8riges in consumption) Dutmore strong and subtle laws are examined: the aocelerat on 0 struo ura 0 es in s oase e e s ype aws are right wi th the more reason). Of oourse, in view of the ohanges in needs and tastes of consumers, tpe interval on whioh the ratios AVjl ~Vj' are growing oan turn out to be shorter than such one on whioh the growth of Vj/vj , is observed.

11 t

For the estimation of the oonvexity

of real, statistically fixed trajectories the following prooedure is used with referenoe to two-dimensional space of vectors v = (Vj " V j ) (for every j separately). Let observations be denoted by index t = = ('r, It + 1, ••• , t' + p, ••• , T) where ~ is the number of an observation on which a certain minimum of consumption is registered (within the gLven series of observations). Real trajectories are oonsidered for which as a rule the following inequality is correct: V;~ (t> t') for all j. Suoh'trajectories are the trajeotories of general oonsumption growth above vt'.

vi

Calculate quantities

vjp= t

v tr +p _ v't 'l-' ( t et').1 ,j v j + v j ,-v j ' -~+p. _ -~-

(3)

vjl - vj '

't t t 't+p ~+p where v j ' v j " v j ., v j ' , v j are statistically registered data; p = (2 , • • ., T- tr); t = (tt +1 , • • ., t' + +p-1). As a oriterion of the convexity of real trajectories on the segment t'+ p] the observation of the following inequality is accepted:

et' ,

We consider the theoretical trajectory as statistically oonfirmed one if (4) is observed in a suffioient majority of real data (i.e. for a suffioient majority of t numbers under given ~ and p).

A oertain evaluation of the monotony

of real trajeotories oonvexity is used. For this purpose the observation of (4) is tested for every p such as 2cP~T - It' and for all t (~+ 1~

Et .. ~+ p - 1).

Wetll demonstrate below the results of tests 3 of real trajectories convexity using personal consumption expenditures statistios of Federal Republio of Germany (aocording to statistioal issues of UNO). We omit the initial data. Table 1 illustrates the technique of oriterion (4) utilization on an example of two artioles: "Food, beverages and tobaoco" (is used as j' one) and "Reoreation, ent erta1nment t eduoation and oultural J Tlie oomputer programme was made by A.V.ShQherbinskaia. L.G.Krivoshapova and E. V.Bal!tskaia have made the oaloUlations.

26

K. K. Val'tukh

TABLE 1

Example of Testing on Critenon (4) 1960

1. Food, beverages and tobacco (Xj ,) 2. Recreation, entertainment, eduoati~n and cultural services (xj ) 3. 4.

:jx. ,T-t' T'" J, -v

1963

1964

1965

1966

1967

76.4

79.0

81.8

83.6

84.4

13.0 13.0

14.7 15.8 1.1

15.5 16.8 1.3

16.7 17.9 1.2

17.3 18.7 1.4

17.8 19.0 1.2

x

x

1

2

3

4

x

x

1

2

3

4

1973

1974

1975

x.J

5. Maximal possible number of positive responses * (smax(p») 6. Actual number of positive responses (Sj(p» 1968

1969

1970

1971

1972

1. 86.2

90.0 20.3 21.2 0.9

94.2 22.1 22.9 0.8

98.1

6 6

7 7

8

100.5 102.3 104.1 104.3 25.4 26.2 26.7 27.0 25.5 26.2 26.9 27.0 0.1 -0.0 0.2 12 10 11 9 11 10 9 9

2. 18.6 3. 19.7 4. 1.1 5. 5

6.

5

23.5 24.5 1.0 7

Sum

x x

x x

78 74

-------_.-- - - ---_._-------------------*For this and the next line the number of year denot es the value of ~ +p.

Souroe of the initial data: "Yearbook of National Acoounts Statistios'1 1971, v.I, p.370; 1912, v.I, p.393; 1976, v.I, p.)14. services" (j). The first two lines of Table 1 contain the statistioal data on the articles. The thir% l~ne shows calculated quantities x. 4 JP obtained by the use of formula (3) under the condition that ~ = 1960 and ~+p=T=1975. The difference between calculated and actual quantities is given in the fourth line of the table. One can see that calculated quantities are greater than actual ones in 11 cases from possible 12, that means the suffioiently high level of oriterion (4) realization. The series of analogous calculations was oarried out under the condition that 1960 was considered eaoh time as year rand consecutively taken years from 1964 to 1915 were considered as (~ + p) ones. We omit here the complete results of these calculations on the reason of their cumbersomeness and gi. ve in Tabl e 1 the summary results only. The fifth line of the ta4 In this case the volume oft the current purohases of goods x j \~th sufficient aocuracy is equaltto the volume of consumed goods vj •

bIe shows the theoretioally possible maximal number of criterion (4) realizations (quantities Smax(p) under the condition that corresponding year is taken as (1: + p): it is equal to the number of observations (years) in interval between ~ and given (1:' + p). For example, if 1964 is taken as ( ~ + p), then testing on cri terion (4) is possible for one observation only, i.e. for 1963; if 1965 is (~+p), then the examinations can be made for 1963 and 1964, etc. The last (sixth) line of Table 1 (quantities Sj(p») shows the gummary number of positive responses on examination for each ( ~ + p). The comparison of the fifth and the sixth li~es shows that inequality (4) is realized for all or at least for· overwhelming majority· of all cases on the whole period from 1960 to 1975. This result can be considered as the oorroboration of oonvexi ty monotony of the real oonsumption growth trajeotory·and, oonsequently, as the corroboration of this traj ec"tory high conformity with the attributes of the theoretioal optimal curve. The indices of oonvexity monotony oan be further generalized. The sum of theoretioally possible positive responses

27

National Economy Models .~A~I,-E

2

Values of SjUl 'C+p

1964 1965 1966 1967 1968 1969 1970 1•

2.

3. 4.

5. 6. 7. 8.

gmax(p) Clothing and footwear Gross rent, fuel and power Furniture, furnishill9 and household equipment and operation Medical care and health expenses Transport and communication Recreation, entertainment, eduoation and oultural servioes Miscellaneous goods and services

The analogous calculations were carried out for all main articles of personal oonsumption expenditures. The article "Food, beverages and tobaooo ft vias taken eaoh time as j ' one. We omit the calculated xjp 5 and bring together in Table 2 only the indices which oharacterize the monotony of oonvexi ty of the real oon sumption trajectories. It is olear that the maximal number of possible positive responses on examinations is common for all j tmder given ('t"+p); such numbers are given in the first line of Table 2. Then the indioes of actual positive responses on the examinations are given. The last table oolumn gives the estimations of the oonvexity monotony for all j. The next to last oolumn shows the indioes under ('l:+ p) = 1975, i.e. oharacterizes the oonvexity on interval from 1960 to 1975. The oonvexity on interval as a whole is strongly enough pronounced in respect of all articles exoluding "Clothing and footwear" and "Transport and oommunication"; for artiole "Medical oare and health expenses" the oonvexity is strongly pronounoed on

5Strictly speaking just xip but not -t Vj are oaloulate d when personal o~EsumPtion statistios is prooessed. See the differenoe analysis below. DMCNE -

s-

7

4

2

3

3

2

6

4

4

2

3

0

2

5

7 1 7

:3 3

4 3

5 5

6 6

7 7

2

5 3 5

2 1

J

J

1

2

1

2

0

1

2

3

0 0

2

2

0

1

1 0

------_.

for all (~+ p) is equal to 78. The aotual number of oases, in whioh the inequality (4) was observed, is equal to 74 (see the gum on the last 00lumn of Table 1). It is obvious that the level of criterion (4) observation is very high.

6

4 2 3

1

~+ P

1971 1972 1973 1974 1975 1•

10 0

11 0

12

78

1

27

9

12

9

8 9

7

9

50 66

1

J

J

2

1

0

9 9

10 10

10

11 1 11 12

8

9

2.

5

6

J.

1

4

4. 5. 6. 7.

8 2

4 7 7

8.

Sum

9

34

27 74 73

See footnotes to Table 1. interval 1960-1975 but it is not monotonous. We oannot give in this report to some extent detailed analysis of oases in whioh the convexity hypothesis is not corroborate by given tests. But we'll make some remarks. For more clear presentation of the prooesses, which, maybe, are expressed in Table 2 too formally, let us oonsider Table 3. The interval is divided there into three segments : 1960-1967, 1967-1971, 1971-1975. The law was formulated above on the growth of ratios iiVj / LlVj , on sufficiently wide intervals of the consumption enlargement. Its adequacy to reality is tested by caloulations shown in Table 3. With respect to this table the following is noteworthy. Table J is built on the base of the data on current purohases of goods and services xi. But the approximate equality xi:::= vi is correct for nondurable goods and servioes only. Por

K. K. Val'tukh

28

TABLE

Personal Incremen S 0 of Increments

I

1. Food, beverages and tobacco

2. Clothing and footwear

J. Gross rent, fuel and power 4. Furniture, furnishingsand household equipment and operation 5. Medical care and health expenses 6. Transport and communioation 7. Recreation, entertainment, eduoation and oultural services 8. Miscellaneous goods and services

oumulated goods as its addenda. Since Table J contains for all kinds of goods the quantities

x;, Lix;, etc., it gives birth to some inacourate ideas about real dynamics of mentioned goods oonsumption. Let us consider the table. In majority of oases the ratios

Li xj

/

c1 Xj

'

demonstrate

the

1960

1967

1971

1975

69.5 23.3 20.9

84.4 31.6 32.2

98.1 39.6 40.0

104.3 41.3 49.1

26.1 15.8

35.2 10.2 28.1

46.5 12.3 41.2

50.5 13.8 44.2

13.0 11.8

17.8 16.8

23.5 22.3

27.0 25.3

7.5

Li x j

durables and semi-durables the

inequality x;~v; is oorrect sinoe v; inoludes earlier ac-

X j

19611967 1. 14. 9 2. 8.3 3. 11.3 4. 9.1 5. 2.7 6. 12.3 7. 4.8 8. 5.0

growth when the transition from 1961-1967 to 1968-1971 as well as the transition from 1968-1911 to 1972-1975 is considered. This faot corresponds to tendencies immanent for funotion D. Let us pay speoial attention to the strong decline of the inorement of personal consumption expenditures in the last period: for 4 years from 1971 to 1975 it was equal to 29 milliards of 1963 FRG marks whereas in previous 4 years - 65.2 m11liard5. Vlhen such process takes p1aoe, it always influences first and foremost on the purohases of durable and semi-durable goods; in the given oase it is as well obvious: Table 3 shows especially strong declines of x j for articles "Clothing and footwear lt , "Purni ture, etc. ", and "Transport and communication" (notioe that the last contains purchases of the personal vehicles including cars).

L1 Xj/ L\ xj

,

19681971

19721975

19611967

1968- 19721971 1975

13.7 8.0 7.8 11.3 2.1 13.1 5.7

6.2 1.1 9.1 4.0 1.5 3.0 3.5 3.0

x 0.56 0.76 0.61 0.18 0.8) 0.32

x 0.58 0.60 0.82 0.15 0.96 0.42

x 0.27 1.47 0.65 0.24 0.48 0.56

0.34

0.40

0.48

5.5

The cause is the very well-known peculiarities of durables and semi-durables. Earlier bought and accumulated exemplars of them are used in consumption in every given year. Correspondingly the new purohases are uged for reimbursement of the removal and for the enlargement of acoumu1ated property: X

t j

= r jt

V

t-1 j

A

t

+Llv j

where r; is the rate of removal

(O<:rt <:1). One can see without dif-

ficuliies that, due to these peculia6The term removal means in this text

the in nature reduoing of earlier accumulated mass of goods.

National Economy Models

29

rities, the v j oan inorease in the oourse of several years in spite of stabilization or even oertain deorease of corresponding xj •

Meanwhile the increase of durables and semi-durables oonsumption in the same period is the sum total of the property inorements in all years of

In PRG in 1975 oompared with 1971 the growth of x j took place for all artioles and among them for such ones that contain the durable and semi-durable soods aa their implicit components (see Table 3). Hence it is more right that the inorement of oorresponding property took plaoe. And it is not excluded that this increment was growing in relation to the increase in food oonsumption. It must be underlined that the last was in 1972-1915 twioe smaller than in 1968-1971.

-Vj(1971)=~~Vjt.

the periOd~ DoVj (1972-1975)-Vj (1975)-

This fact t=1972 oan play a decisive part in determi-

nation of the ratios

~Vj,(1912-1915)=Vj,(1975)-Vj,(1971)= t

(1975)-xj

t

/

.6V j ,.

Certain conventional oaloulations were carried out for the estimation of real possibility of the ratios 6Vj/ ~Vj' inorease in the period of 1972-1975 in oomparison with 19681971 one.

It must be taken into aooount as well that the inorement of consumption of food (and any nondurable goods, of course) is determined as the difference between purchases of suoh goods in oorresponding years: = xj

.6V j

Consider first of all the artiole "Furni ture t furnishings and household equipment and operation" which apparently oontains the durables in more share than any other one. t Let in 1967-1975 the division of x . for J t t-1 and UA v t was as follovdng: rjv j

j

(1971 )=~Xj t (1972-1975)

(thousand million of 1963 FRG marks)

x~

1967 35.2

1968 36.0

1969 39.4

1970 43.3

1971 46.5

1972 49.2

1973 50.3

1974 49.3

1915 50.5

r jt v t-1 j

29.0

31.0

33.0

35.0

37.0

39.5

42.0

44.5

47.0

6.2

5.0

6.4

8.3

9.5

9.1

8.3

4.8

3.5

J

~V;

Thus it is acoepted in the calculation that the removal of aooumulated property rose on 2 milliards of marks per year in 1968-1971 and on 2.5 milliardsper year in 1972-1915; it seems not underestimated assumption. We think as well that the conventional preposition conoerning the share of

~V; in

x; for the initial year (1967)

is not essentially overestimated. The result springs up that in 1968-1971 the inorement of corresponding proper-

ty was equal to 29. 2 milliards of FRG marks and in 1972-1975 - to 26.1 milliards. It means the growth of this inorement in ratio to the in crease of food consumption which was equal to 13.7 milliardsin 1968-1971 and to 6.2 milliar~in 1912-1975. In our opinion it is very probable that the calculation is approximately adequate to the real process. Carry out the analogous calculation for the article "Transport and communication tt : (thousand million of 1963 FRG marks)

x jt

r; v;-1

~v~ J

1961 28.1

1968 30.0

1969 34.1

1970 39.3

1971 41.2

1972 42.0

1973 43.1

1974 40.8

1915 44.2

26.0

21.0

28.0

29.0

30.0

31.5

33.0

34.5

36.0

2.1

3.0

6.7

10.3

11.2

10.5

10.1

6.3

8.2

The increment of accumulated property is equal here to 31.2 milliardS of marks in 1968-1911 and to 35.1 milliar&in 1972-1975. The growth of this inorement in ratio to the increments of food oonsumption is obvious.

At last for the article "Clothing and footwear" the following oaloulation seems to us sufficiently realistic:

K. K. Val'tukh

30

(thousand million of 196) FRG marks) x jt

rj

t1

v;-1 t vj

1967

1968

1969

1970

1971

1972

1973

1914

1915

31.6

32.8

35.3

37.0

39.6

41.3

40.8

40.4

41.3

30.0

31.0

32.0

33.0

34.0

35.5

37.0

38.5

40.0

1.6

1.8

3.3

4.0

5.6

5.8

3.8

1.9

1.3

The increment of accumulated wardrobe is equal to 14.1 milliards of FRG marks in 1968-1911 and to 12.8 milliards in 1972-1915. ThuB in this case we shall state the growth of~vj /~v.,,, too. . J Come back to Table 2 now. It shows that thetexaminations, in whioh the values x j were processed, do not oorroborate the convexity hypothesis in cases of two articles with high share of durables and semi-durables: "Clothing and footwear" and "Transport and communication". Now we have the reasons for assertion that the cause is just the use of quantities x jt instead of v jt • But function D, the peculiarities of which ere tested, is constructed just as function of vector v, not of vector x. It is very probable that, if we use the quantities v. on mentioned kinds of consumPti~n, then we'll obtain the high degree of real trajectories correspondence to the properties of function D. As regards the article "Medical care and health expenses", the correct estimation of the calculations result requires to analyse the relation between private and public expenditures on these aims. But we cannot carry out such calculations. As a whole we consider the oaloulations for FRG ae sufficiently satisfactory ones. Analogous examinations haTe been carried out on personal consumption expenditures statistics for 14 developed capitalist oountries (Australia, Austria, Belgium, Canada, Denmark, Greece, FRG, Finland, Italy, Norway, Spain, Sweden, United Kingdom, USA) and for 5 developing countries (Jamaica, Panama, Puerto Rico, Thailand, Venezuela). Here we give the results bearing immediately on the quantities

xi,

not on any conventional v.j or~vj whioh were oalculated for FRG. As a whole the oriterion (4) has been observed in more than 70 per cent of oases both in examinations of the oonvexity of real trajectories within sufficiently wide intervals (8 to

18 years for various countries) and in tests of oonvexity monotony. Some especially suooessful results of

the examinations have been obtained in investigations on the budget statistios of Hungary and Austria, aa well ae on Austrian statistics of acoumulated consumer's property (more than 80 per cent, and in some oases about 100 per cent of positive responses on tests using criterion (4».

To all appearance, the hypothesis on the utility function can be considered at present as in sufficiently high degree corroborated with the mass faotual data. In other words, the function can be considered as sufficiently olose expression of an utility measuring law acting in the real behaviour of mass consumer. REFERENCES

A. r., K.K. BanbTYX (pe~.) ~cno~b30B8HHe H8ponHOXo3H~CTBeHHHX Monene" B nnSHHpoB8HHH. 8XOHOMHX8, MOCKBa. 232 CTp.

AraH6erHH~

(1975).

1!Pplication of National Eoonomy Models in Planning). BanbTyx, K. K. (pe~.) (1972) MeEoTpa-

cneBow 6anaHc

nBOH3Bo~cTBeHH~x

¥~~HOCTeB. ~~H rgk~, ~o~Ba. CTR. (erind~str; Balance of Pro uctive caJacities). Waltuch, K. K. (1972 • EntWioklungsEroEortionen und Befriedi~

der Bedurfnisse •. Verlag Di~irtschaft, Bert1n 161 SS. BanbTyx, K. K. 19~3}. YXOBneTBopeHHe

06meCTB8 H YonenHpoBaHHe HsponHoro X03HHCTBa. HayR8, HOBOCHOHpCK. 318 CTp.

nOTpe6HOCTe

(Satisfaction of Society Needs

and National Economy Modelliif>.

Val'tukh, K. K. (1975). A theore~­ cal model of mass consumer behavior and some methodological problems of social studies. Quali ty and Quantity, 9 t Amsterdam. pp. 323-337.