A demand and supply model of economic growth

D E E C O N O M I S T 121, N R . 6, 1973

A D E M A N D AND S U P P L Y M O D E L

OF E C O N O M I C G R O W T H 1 , 2

B Y

S. K. K U I P E R S *

1 MAIN T R E N D S IN P O S I T I V E G R O W T H T H E O R Y

The aims of this article are to develop a demand and supply model of economic growth and to investigate the features of the growth process generated by this model. Above all, attention will be paid to the following questions:

(i) Does a tendency to 'equilibrium' growth exist in the sense of capital and labour being fully utilized, the price level remaining constant with time, and the market of produced goods being in equilibrium ?

(2) If so, what are the equilibrating mechanisms; if not, what are the causes of growth disequilibrium ?

(3) What are the determinants of distributive shares ? In modern positive growth economics developed since the second

world war, two main trends may be distinguished: models of equilibrium growth and models of disequilibrium growth. As distinct from the former class of models, disequilibria do not disappear infinitely fast in the latter. It may even be that an equilibrating mechanism is lacking sothat the disequilibrium does not disappear at all.

Two important schools of thought have developed the theory of equilibrium growth: the neo-classical and the neo-keynesian.

* Assistant Professor (wetenschappeli jk medewerker) of Economics, University of Gro- ningen, Tile Netherlands.

1 The author is indebted to Professor Frits J. de Jong for his non-desisting support during the preparation of this paper. He is grateful to Mrs. Gerda H. de Jong of Veendam, The Netherlands, and to Dr. James H. Gapinski, Assistant Professor, Florida State Uni- versity, Tallahassee, Florida for kindly improving the English of this article.

In many respects this article draws heavily upon my doctoral dissertation: De be- tekenis van vraag- en aanbod/actoren in groeimodellen met ddn sector, mimeographed, Gro- ningen, 1970.

554 s.K. KUIPERS

Adherents of the neo-classical school are Solow (1956), a Swan (1956),4 and Meade (1962) 5; writers belonging to the neo-keynesian school are Kaldor (1957, 1961), 6 Mrs. Robinson (1956, 1964), 7 Pasinetti (1962),8 and Kregel ( 1971 ). 9

Neo-classical and neo-keynesian growth models differ with respect to the mechanism by which full employment is provided. In the neo-classical theory it is assumed that labour and capital are substitutable according to a continuous aggregate production function. Unemployment induces a fall in the real wage rate, and this leads to the substitution of labour for capital until unemployment has disappeared. Equilibrium in the market of produced goods is guaranteed by an automatic adjustment of investment to savings.

Most neo-keynesian authors deny the existence of an aggregate production function and, by denying this, the possibility of substitution between labour and capital. Moreover, the real wage rate is not determined in the labour market, as it is in the neo-classical theory, but rather in the market of produced goods. Unemployment will, first of all cause a fall in the money wage rate. At the same time, however, the price level will decrease due to an excess supply in the commodity market. It is assumed that the fall in the price level will be greater than the fall in the money wage rate. Hence, the real wage rate and the labour share of the national income will increase. As the proportion of consumption out of labour income exceeds that out of capital income, the level of consumption demand increases. As a consequence of this, unemployment will disappear.

Both in the neo-keynesian and in the neo-classical theories, it is assumed that the adjustment process is so fast as to justify the focus of attention on the equilibrium development of the economy. Disequilibrium can only exist in the short run. In the longer run disequilibrium will have disappeared. On the other hand, authors

3 R. M. Solow, 'A Contribution to the Theory of Economic Growth,' Quarterly Journal o] Economics, LXX (1956), pp. 65-94.

4 T. W. Swan, 'Economic Growth and Capital Accumulation, ' Economic Record, X X X I I (1956), pp. 334 361.

5 j . E. Meade, A Neo-Classical Theory o] Economic Growth, London, 1962. 6 N. Kaldor, 'A Model of Economic Growth,' Economic Journal, LXVII (1957), pp.

591-624; N. Kaldor, 'Capital Accumulation and Economic Growth,' The Theory of Capi- tal, F. A. Lutz and D. C. Hague ed., London, 1961, pp. 177-222.

7 Joan Robinson, The Accumulation o] Capital, London, 1956; Joan Robinson, Essays on the Theory of Economic Growth, London, 1964.

8 L. L. Pasinetti , 'Rate of Profit and Income Distribution in Relation to the Rate of ECOllomic Growth,' Review o/ Economic Studies, X X I X (1962), pp. 267-279.

9 j . A. Kregel, Rate of Pro]it, Distribution and Growth: Two Views, London, 1971, esp. Ch. 12.

A DEMAND AND SUPPLY MODEL OF ECONOMIC GROWTH 5 5 5

developing the idea of disequilibrium growth do not hold such an optimistic view. The most pessimistic among them - e.g., Harrod (t939, 1948), l° Domar (1946, 1947), 11 Duesenberry (1958), 12 Phil- lips (1961), 13 Bergstrom (1962), 14 and Rose (1966)15 even go so far as to deny the necessity of forces of adjustment to bring about equilibrium growth eventually. Others - e.g. Williamson (1970)16 _ do accept the point of departure that equilibrium will eventually be restored but reject the idea that disequilibrium is only a short-run phenomenon.

The present author feels that it is not sensible to confine growth theory to an explanation of the equilibrium development of the economy because history shows too many disequilibria which do not disappear. One may think, for instance, of the situation of capital shortage that ended in most Western countries about 1914, of the situation of capital abundance between the two world wars, and of the permanent inflation after the second world war. 17 To be able to explain these lasting disequilibria, it is not possible to confine growth theory to a theory of equilibrium growth.

The concept of a lasting disequilibrium is not independent of the period which underlies the analysis. As will be apparent in section 3, growth theory is defined as a study relating to a period in which capital goods do not depreciate fully but in which investment causes an increase in the stock of capital. This period will be called the intermediate period. Lasting disequilibria can then be defined as those disequilibria which do not disappear within the intermediate period. As distinct from these, short run disequilibria disappear approxi-

10 R. F. Harrod, 'An Essay in Dynamic Theory, ' Economic Journal, XLIX (1939), pp. 14-33; R. F. Harrod, Towards a Dynamic Economics, London, 1948.

11 E. D. Domar, 'Capital Expansion, Rate of Growth and Employment , ' Econome- trica, XIV (1946), pp. 137 147; E. D. Domar, 'Expansion and Employment , ' American Economic Review, X X X V I I (1947), pp. 34-55.

12 j . S. Duesenberry, Business Cycles and Economic Growth, New York, 1958. la A. W. Phillips, 'A Simple Model of Employment , Money and Prices in a Growing

Economy, ' Economics, N.S. , X X V I I I (1961), pp. 360-370. 14 A. R. Bergstrom, 'A Model of Technical Progress, the Production Function and

Cyclical Growth, ' Economics, N.S. , X X I X (1962), pp. 357-370. la H. Rose, 'Unemployment in a Theory of Growth,' International Economic Review,

VII (1966), pp. 260-282. 16 j . Williamson, 'A Simple Neo-Keynesian Growth Model,' Review o/ Economic

Studies, X X X V I I (1970), pp. 157-171. 17 In a s tudy o5 unemployment in Great Bri ta in during these periods, Matthews comes

to the conclusion tha t unemployment before 1914 was for the greater par t due to capital shortage, whereas between the world wars it was caused by a shortage of effective de- maud. In the post-war period there is neither capital shortage nor demand shortage for the first time. R. C. O. Matthews, 'Why has Bri tain had Full Employment since the War?, ' Economic Journal, L X X V I I I (1968), pp. 555-569.

5 5 6 S. K. KUIPERS

mately within this period. Finally, lasting disequilibria may be di- vided into long run and permanent disequilibria. The former will disappear, though not within the intermediate period; the latter, however, will remain.

On the strength of the above, equilibrium models of economic growth must be rejected as being not realistic. The disequilibrium models mentioned above are not open to these objections. They may, however, be criticized in another respect. This criticism refers to the way in which the theory of income distribution is specified. In the models of Harrod, Domar, and Duessenberry, this theory is entirely lacking, while in Phillips' model it is rather rudimentary. The theory of income distribution in the models of Bergstrom, Rose, and Williamson is of a neo-classical nature: labour is rewarded according to its marginal productivity. As the underlying assumptions of profit maximization and perfect competition are not realistic, is these models must also be rejected.

The disequilibrium models of economic growth have still another characteristic which makes them less realistic. This is the fact that, according to these models, output will always adjust itself to effective demand in a Keynesian manner as long as capacity limits do not prevent it from doing so. In this sense these models are demand oriented. In reality, however, this adjustment will not occur if profit margins are too low. When the profit margin is sufficiently high, it is quite reasonable to assume that output will not be restricted by supply considerations: total demand will be satisfied. When, on the other hand, profit margins are relatively low, profit positions may give the entrepreneur cause for concern. To improve the profit margin he will economize on labour. The average labour productivity will be increased by this so that at a given real wage rate the profit margin will also increase. Under these circumstances output is no longer determined by effective demand but by effective supply. Excess supply in the iabour market is accompanied by excess demand in the market of produced goods.

To meet with the above objections, the demand and supply model to be developed in this paper should have the following main characteristics.

(1) Growth is not necessarily balanced. (2) The neo-classical theory of income distribution is replaced by

a theory according to which money wages and prices are the result is j . L. Bounla, Ondernemingsdoel en winst, Leyden, 1966, pp. 1-3 and pp. 72-87.

A DEMAND AND SUPPLY MODEL OF ECONOMIC GROWTH 557

of a process of wage negotiations. Workers seek a certain value of the labour share in the national income; entrepreneurs a certain value of the profit margin.

(3) Output may be determined by effective supply as well as by effective demand.

The analysis will be confined to a closed economy without a sepe- rately specified public sector and without a monetary sector.

The plan of this article is as follows. In section 2 the symbols to be used are defined. In section 3 the model is developed. In section 4 the short run characteristics of the model are examined. In section 5 the properties of the process of steady growth are enunciated, while in section 6 we shall go into the stability of the process of steady growth.

2 LIST OF SYMBOLS

_/t t

Ct Et Et ct

gt gt It it Kt K; Mt 74~ t

Nt Nt ~bt

Pt

qt f t

St s t

u t

Wt

state of arts with respect to the efficiency of labour; real consumption demand; employment of labour in efficiency units; total labour force in efficiency units; employment of labour in efficiency units per unit of capital; total labour force in efficiency units per unit of capital; degree of excess demand in the market of produced goods; real investment demand; investment quota; capital stock; desired capital stock; nominal stock of money; liquidity quota; employment of labour in natural units; total labour force in natural units; labour intensity; price level; real gross profits; gross profit margin, capital share of national income; rate of profit; total real savings; average propensity to save; rate of unemployment; money wage rate;

558 S. K. K U I P E R S

Wt

Xt

Xt

XmC*X, t

Xma;x, t

Yt Zt %t

8t g

mt

Vt

~t Yet

09t

real Wage per unit of labour in efficiency units; total real output; actual average capital productivity; technically determined maximum average capital productivity; average capital productivity at full employment; total real demand for produced goods; total real labour income; labour share of national income; rate of labour-augmenting technical progress; growth rate of employment of labour in efficiency units; growth rate of the labour force in efficiency units; growth rate of capital stock; growth rate of employment; growth rate of the labour force; growth rate of output; relative rise in the price level; relative rise in the nominal wage rate.

A dot over a variable indicates the derivative with respect to

time; e.g., Kt = dKt dt

3 THE MODEL

3.1 The Demand Model

Only one good is produced, and it may be used either as a consumption good or as an investment good. Total real demand Yt is equal to the sum of real consumption demand Ct and real investment demand It:

Y t = Ct q:- It. (3.1.1)

For simplicity depreciation is assumed to be zero; gross investment and net investment are therefore equivalent.

It is assumed that labour income will be consumed entirely and that only a certain proportion of capital income, c2, is consumed, l0

Ct = Zt q- c2Qt, 0 < c2 < 1. (3.1.2)

19 C. A. van den Beld, Dynamiek der ontwikkeling op middellange termijn, inaugural lecture, Rotterdam, 1967, p. 23.


By real savings is meant the difference between total income and consumption:

St = X t - - Ct. (3.1.3)

The national income consists of wages and profits:

X t = Z t + Qt. (3.1.4)

Equations (3.1.3), (3.1.4) and (3.1.2) yield

St = (1 -- c2)Qt; i.e.,

(3. !.5)

(3.1.6)

neo-keynesian

St = s2Qt, 0 < s2 <= 1.

This is the classical savings function as used in growth and distribution theory. 2°

Investment demand is determined according to the capacity adjustment equation developed by Chenery (1952) 21 and Koyck (1954) 2~:

I t = # (K~ -- vKt) , 0 < /~ ~ 1; v > O. (3.1.7)

In this equation K t is the actual capital stock and K~ the desired capital stock; # and v are the adjustment parameter and the anticipation parameter respectively. In a process of steady growth, in which the growth rate of capital stock is constant, equation (3.1.7)

K; describes a linear relation between - - and v. According to this equation one may write K t

K2 - v + - - , ( 3 . 1 . 8 )

Kt #

where x is the steady growth rate of the capital stock. Equation (3.1.8) is sketched in Figure 3.1.1 for ~ = 0.04 and # = 0.20.

Figure 3.1.1 shows that equality between the desired and tile actual capital stock is not a necessary condition for steady growth: K~ may be smaller or greater than Kt. The actual capital stock greater than or equal to the desired capital stock is compatible with steady

20 See, e.g., Kaldor (1956), Robinson (1970), and Weintraub (1966). N. Kaldor, 'Al- ternative Theories of Distribution,' Review o~ Economic Studies, X X I I I (1956), pp. 83- 100, esp. pp. 94-100. Joan Robinson, 'Harrod After Twenty-One Years,' Economic Journal, LXXX (1970), pp. 731 737. S. Weintraub, A Keynesian Theory o/Employment, Growth and Income Distribution, Philadelphia and New York, 1966, pp. 89-101.

21 H. B. Chenery, 'Overcapacity and the Acceleration Principle,' Eco~cometrica, XX (1952), pp. 1-28.

22 L. M. Koyck, Distributed Lags and Investment Analysis, Amsterdam, 1954.

560 S. K. K U I P E R S

Kt

Kt

- 0 . 1

- 0.2

-0.3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Y

i i i

1.3 1j

Figure 3.1.1

growth if v < 0.8. For v < 0.8, entrepreneurs obviously build ahead of demand for capital" they anticipate the further rise in the desired stock of capital. Apart from the anticipation motive, there may be a second reason why entrepreneurs invest even though K~ is greater than or equal to K~. This is the precautionary motive" to avoid a situation of capacity shortage entrepreneurs retain a certain proportion of the capital stock as a stand-by.


In the s t a t ionary state, where ~ = 0, there is no reason to do so. The desired capital stock K[ will then be equal to Kt, which implies tha t vt = 1.0.

The desired capital s tock exceeds the actual stock if v > 0.8: en t repreneurs are catching up with the demand for capital. If v - 1,

then according to Figure 3.1.1, K [ _ 1.2. Kt

On the s t rength of the above, it m a y be concluded tha t v is a measure for the ant ic ipat ion behaviour of entrepreneurs . Small values of the ant ic ipat ion paramete r imply a high degree of anticipation. High values of v - v > 0.8 in our example - mean tha t ent repreneurs do not ant ic ipate at all.

The desired capital s tock is assumed to depend on (1) the expected level of output , which will be assumed to be

to actual ou tpu t ; the amount of real gross profi ts; the l iquidi ty of the economy. econometr ic model building these factors tu rn out to be the

equal (2) (3)

F r o m crucial de terminants of investment . 2a

The following specification is chosen 24:

K; Kt K t ' K t ' PtXt ' (3.1.9)

H y > 0 ; HQ > 0 ; H M > 0 . K K P Y

In this equat ion Mt is the nominal stock of money and Pt the price

Xt Ot Mt , 7 and - - are the average capital level. The ratios Kt Kt PtXt

product iv i ty , the rate of profit , and the l iquidi ty quota, respectively. The funct ion H will be assumed to be homogeneous of degree v in

Xt and Qt . For cer ta in reasons, which will be made clear below, K t Kt

v is assumed to be posit ive and less t han one:

0 < v < I. (3.1.I0)

2a See, fo r i n s t a n c e , V a n d e n Beld (1967), p. 23, a n d Centraal economisch plan, The H a g u e , 1971, pp. 185-186.

24 T h e f i rs t d e r i v a t i v e of a f u n c t i o n y(x, z) wi th r e spec t to x is w r i t t e n y , ; t h a t wi th r e spec t to z is w r i t t e n yz. T h e s e c o n d d e r i v a t i v e of y wi th r e spec t to x is w r i t t e n y x , ; t h a t w i th r e s p e c t to z is w r i t t e n yzz.

562 s.K. KUIPERS

The substitution of equation (3.1.9) in equation (3.1.7) yields

I t = # [ H ( XtKt' Kt'Qt PtxtMt ) K , - - v K t ] . (3.1.11)

This equation may also be expressed as 25

It = #~X~ H ( 1 , XtQt , PtxtMt ) - -#vKt . (3.1.12)

Xt ' PtXt ' Xt ' Pt~-XtJ' qt for ~ [ and as-

suming the liquidity quota to be constant and equal to m, one obtains

x~ It = # ~ h(qt, m) -- [~vKt. (3.1.13)

Writing il for ,u and iz for #v, we obtain

X v I t " t = ~ i~ t_ 1 h(qt, m) -- izKt,

(3.1.14)

0 < v < l ; i 1 > 0 ; i 2 > 0 .

With respect to the function h(qt, m), it will further be assumed that

ha>O,

h¢~ < O, (3.1.15)

hm > 0, and

h = 0 for qt=O.

Entrepreneurs adjust output to total demand:

Xt = Yr. (3.1.16)

The demand model now consists of the equations (3.1.1)-(3.1.4), (3.1.14), and (3.1.16). This model may be reduced to

. X ~ s2Qt = * l~ t_ l h(qt, m) -- i2Kt. (3.1.17)

~-~ This follows f rom the fac t t h a t H is homogeneous of degree v in Xt and --.Qt A Kt Kt

Iunetion/(x,y, holnogeneousof degreev inxandymaybewr i t t enaskV , (@,Y- - ) .


Dividing this by Xt one obtains

s2qt = ilx~- * h(qt, m) -- i 2 - - t (3.1.18)

X t '

where xt is the average productivity of capital• Equation (3.1.18) describes the set of all possible combinations of

the profit margin and the average productivity of capital associ- ated with equilibrium in the market of produced goods.

St Since the propensity to save st = - - is a function of only qt and

I t X t the propensity to invest it = X~t is a function of qt and xt, the slope of (3.1.18) is equal to

~st ~it

dxt ~qt ~qt - - ( 3 . 1 . 1 9 )

dqt ~it

~xt

From equation (3.1.18) one may write

• v - - 1 dh(qt, m) S 2 - - ~ l X t

dxt dqt

dqt il(v -- 1)x~-2J~(qt, m) @ i2. x~

(3. I. 20)

The sign of the denominator of (3.1.20) is

ail 0,or ,O[ 11 axt i1(1 -- ~h(qt, m)

The sign of the numerator of (3.1.20) will be derived graphically. In Figure 3.1.2, the diagrams of st and it as functions of qt are

presented for three given values of xt; namely, x3 > x2 > xl. Ac- cording to equations (3.1.6) and (3.1.14), st is proportional to qt and

~it . it is a decreasing function of qt. The derivative - - 1s supposed to

~ x t

be negative. Under these circumstances an increase in xt will make the investment curve fall. Figure 3.1.2 shows that in this case xt is an increasing function of qt for qt < 3 and a decreasing function for qt > q. Average capital productivity reaches its maximum for qt = 3. For this reason the function x(qt) has a maximum for qt = ~ in the

564 S. K. KUIPERS

st

it

~ t i ( xl 1

'/ c] q t

zzt

Figure 3.1.2

I " 1 1 ~-. In an analogous manner it may region xt > i1(1 _ 42v)h(q.t, m) J [ i2 1 1

be shown that in the region xt < , [ ~1(1 - - ~ m) | Y ' the func-

tion x(qt) has a minimum for qt = 4. Equation (3.1.18) can now be sketched. This has been done in Figure 3.1.3.

It can easily be checked that within the oval investment is greater than savings and out of it investment is less than savings. Thus within the oval the market of produced goods is in excess demand and out of it in excess supply. For instance, in the region

xt > I il(1-- v))h(qt, m) ] ~

a fall of xt at a given qt makes it increase \~xt- < 0 but leaves st

unchanged so that it will become greater than st. Excess demand in the market of produced goods causes a rise in

output. In the short period - in which the capital stock is constant -


xt

i t < s t

B it < st

~ ~ u . (3.1.18)

i

i iD I ,

q

Oi t Ox-~ = 0

y

qt

Figure 3.1.3

this implies an increase in average capital product iv i ty . Average capital p roduc t iv i ty will decrease in case an excess supply should exist. These ad jus tments imply tha t points on the curve ABC are stable and tha t points on the curve ADC are unstable. I t can now be seen why it is impor t an t to assume 0 < v < 1.26 An area in

which ~i~ - - - < 0 will only exist under this assumption. Should v be c~xt

greater t han or equal to 1, then, according to equat ions (3.1.19)

Kt ( aXt ~ 26 Empirical investment equations of the type Kt-~- ~ \K~t-1/ (0 < /~ < 1) do

have this property. In this function a is the desired capital coefficient and F is the ad- a / t

justment parameter. This equation may indeed be written as It Xt I~ -- Kt-1. Kt_ l I~-1

Since 0 </~ < 1, the relation between It and Xt in this equation corresponds with that in equation (3.1.14). For the above type of investment equation, see e.g.B.G. Hickman, Investment Demand and U.S. Economic Growt]~, Washington, D.C., 1965, esp. Chapters 2 and 3.

566 s.K. KUIPERS

0it and (3.1.20), - - would always be positive. In this case the curve

8xt of xt as a function of qt would have the shope ADC for all values of xt and qt, and an equilibrium in the commodity market would always be unstable. Since this is not likely to be realistic, it is es- sential to assume 0 < v < 1.

3.2 The Supply Model

3.2.1 The P r o d u c t i o n E q u a t i o n

The production equation gives a description of the production structure. The production structure is characterized by the degree of substitutability between capital and labour and by the homogeneity or heterogeneity of the capital goods in the course of time.

The degree of substitutability is not independent of the period which underlies the analysis. Three periods may be distinguished:

(1) in the short period capital goods do not depreciate fully and investment has only an income effect and no capacity effect;

(2) in the intermediate period capital goods still do not depreciate fully but investment does have a capacity effect;

(3) in the long period investment has a capacity effect and there is full depreciation of capital goods. As mentioned in section 1, growth theory will be taken as a theory of the intermediate period. This means that not only new but also already existing capital goods are employed in the production process. The latter are produced for a certain labour-capital ratio, but this does not necessarily imply that the labour-capital ratio is entirely fixed. Many authors hold the opinion that the labour intensity ex post may vary somewhat, 27 although not to the same degree as when capital goods would not have been designed.

The labour-capital ratio may be changed in three different ways: (1) by a change in the running speed of machines; (2) by reconstructing existing machinery; (3) by a change in the amount of stand-by capacity and in the

number of operating-hours per machine.

z7 See, for instance, the views oI Hicks, Mrs. Robinson, and Solow as contained in the report on the discussions during the Corfoe-conference, in The Theory o/ Capital, F. A. Lutz and D. C. Hague eds., London, 1961, pp. 365 and 366. R. M. Solow, 'Heterogeneous Capital and Smooth Production Functions: An Exper imenta l Study, ' Econometrics, X X X I (1963), pp. 623-645, esp. pp. 623 and 624. D. M. N. van Wensveen, De kapitaal- co~[ficiint van de Vere•igde Staten, Rotterdam, 1966, pp. 110 and 111.


Only in the first two cases substitution occurs. 2a In the third case the crew of a running machine does not change. In this article the analysis will be concentrated on substitution of labour for capital and vice versa. The stand-by capacity as a proportion of total capacity and the number of operating-hours per machine will be assumed to be constant, unless stipulated otherwise. ~9

Although a change in labour intensity by means of a deviation in the running speed of machines from the running speed as foreseen by the mechanical engineers who designed the machines is possible, it wiI1 involve a loss of production. The fact that capital goods are designed for a certain labour intensity implies that production at this intensity is optimal in the sense that any deviation from this intensity will cause a rise in physical labour cost per unit of output. Should one have had the opportunity of producing by means of newly constructed capital goods especially designed for the devi- ating labour intensity, then the average labour cost would have been lower.

Each labour intensity for which capital goods are constructed implies the application of a certain technique of production. However, the number of applicable production techniques will not be un- limited. The set of these techniques indeed depends on the technical knowledge, and the state of arts has an upper limit at the moment the capital good is constructed. Since the possibility of lowering the labour intensity depends on a more advanced technical knowledge, the labour intensity will have a lower limit at any time. a° On the other hand, the relation between technical progress and capital intensity necessitates a minimum capital intensity in order to utilize a given state of arts. al This implies that each state of arts not only implies a minimum but also a maximum boundary of the labour intensity. Hence, the possibilities of substitution even for new capital goods must be considered to be bounded. Formulated more pithily:

28 Changing the labour-capital rat io by means of changes in the running speed of machines is stressed ill E. Gutenberg, GrundlLzgen der Betriebswirtscha/tslehre, Erster Band, Die Produktion, 13th edition, Berlin etc., 1967, pp. 314-325. Krelle thus refers to 'Gutenberg production functions ' : W. Krelle, Produktionstheorie, Ttibingen, 1969, pp. 41-54.

29 A study which focuses entirely on changes ill the labour-capital ratio by means of changes in the number of operating-hours per machine is R. Marris, The Economics of Capital Utilization, Cambridge, 1964.

3o The same view is held by SaIter (1960). W. E. G. Salter, Productivity and Tech~*ical Change, Cambridge, 1960, pp. I3-16.

81 See also Kaldor (1957), p. 595.

568 s.K. IiUIPERS

ex ante substitutability is 'bounded.' Once the capital good has been installed, the possibilities of substitution have become still less: ex post substitutability is 'very bounded.' It follows from the exposition given above that substitutability is simultaneously bounded and very bounded in the intermediate period. It is 'bounded' with respect to new and 'very bounded' with respect to old capital goods. In the short period, in which production occurs solely by means of old capital goods, substitutability is entirely 'very bounded.' In the long period, in which only new capital goods that have been installed at the beginning of the period are being utilized, substitutability is entirely 'bounded.'

The second characteristic of the production structure, as has already been mentioned at the beginning of this section, refers to the homogeneity and heterogeneity of the capital goods. The capital stock is called 'homogeneous' if it is always possible to use all capital goods with the same efficiency in all production processes. In growth literature one form of heterogeneity is prominent - heterogeneity in time. In the intermediate period capital goods of different vintages may differ either with respect to the knowledge in- corporated in them or with respect to the labour intensity for which they are constructed. The former is only possible if technical progress is embodied and is capital-augmenting. Capital goods of the same vintage are homogeneous. Growth theories with a heterogeneous capital stock are called 'vintage models.'

With respect to the labour intensity for which capital goods are constructed, it is possible to make two different assumptions:

(1) that all capital goods are constructed for a labour intensity fixed at the beginning of the long period (complementarity ex ante) ;

(2) that possibilities of choice exist within the intermediate period (bounded substitutability ex ante).

It may easily be proved that equality of labour intensities ex ante and ex post for all vintages is a sufficient condition for the existence of an aggregate production function.a2 For simplicity this equality will be assumed in this article. In this case a stable relation exist among output, employment, and capital stock for a given state of arts. Since substitutability in the older vintages is very bounded, this relation allows for very bounded substitutability in the intermediate period.

a2 F o r a p roof , see K u i p e r s (1970), C h a p t e r 2.


For a given state of arts the production equation may be written as

Xt = F(Nt, Kt). (3.2. t)

This function has the following properties" (1) it is linearly homogeneous in labour (Nt) and capital (Kt); (2) the marginal productivities of both labour and capital are

non-negative in the interval

Nt n* <~ ~ nma:e. (3.2.2)

- - K t

If and when firms are striving for maximum net profits, substitution is only possible within this interval, which will be called the 'substitution interval.'

(3) The marginal productivities of labour and capital, FN and FK, are decreasing functions of labour and capital, respectively:

FNN < O, (3.2.3)

FKK < O.

(4) The labour intensity at which capital goods are constructed is n**. The straight line through the origin in the N--K-plane, the slope of which is n**, is called the efficiency ray.

The production function is sketched in Figures 3.2.1 and 3.2.2. In Figure 3.2.1 an isoquant (or isoproduct curve) is sketched. The

rays (~) and (~) are the 'isoclines.' On the isocline (e) the marginal

Nt

/ / ( Y )

, / " /(B)

Figure 3.2.1

y

Kt

570 S. K. KUIPERS

x t

Xrnax

X ~

nmi n n * n ~ nrnaxn t

Figure 3.2.2

labour productivity is zero; on the isocline (~) the marginal capital productivity is zero. Within the isoclines both the marginal labour and the marginal capital productivity are positive. Hence, under profit maximization substitution is possible only within the isoclines. The ray (,() is the efficiency ray. Xt

In Figure 3.2.2 the average capital productivity, x t - is Nt Kt '

sketched as a function of the labour intensity, nt = - - . Since the Kt

production function is homogeneous of degree 1, the production curve is stable. The substitution interval is n* < nt ~_ nmax. As ap- pears from the diagram, the marginal labour productivity is non- negative. It may easily be proved that in this interval the marginal capital productivity is also non-negative.

According to Euler's theorem, equation (3.2.1) may be written as

Xt = FN, tNt + FK, tKt. (3.2.4)

From this equation the marginal capital productivity can be expressed as

FK, t : Xt(1 - - eXN, t). (3.2.5)


In this equation exlv, t is the labour elasticity of production; i.e.,

N t exlv, t = F a r , t X ~ (3.2.6)

In the interval nm~n < nt < n* the marginal labour productivity exceeds the average labour productivity, and thus the labour elasticity of production is greater than one. Hence, in this interval the marginal capital productivity is negative. In the interval n* < < nt < nmaz the value of ex~v, t lies between 0 and 1. Thus in this interval the marginal capital productivity is positive.

The average capital productivity may vary between 0 and xmax.

In the interval 0 < xt < x*, the marginal labour productivity is positive, whereas the marginal capital productivity is negative. In the interval x* < xt < Xmc~z, both marginal productivities are positive. The marginal capital productivity is zero if xt = x*, while the marginal labour productivity is zero if xt = x~c~z. The average capital productivity xt = x** is the capital productivity corresponding to the labour intensity nt = n** for which the capital goods are constructed.

In this article technical progress will be assumed to be disem- bodied and to be labour augmenting. The production equation may then be written as

X t = F ( A t N t , Kt ) . (3.2.7)

In this equation A t is the state of arts with respect to the efficiency of labour. The analysis given above is not modified by introducing this kind of technical progress. The only thing one has to do is to replace labour in natural units, N t , by labour in efficiency units, E t = A t N t .

3.2.2 T h e S u p p l y E q u a t i o n

In section 3.1 it is assumed that entrepreneurs adjust output to effective demand. Effective demand is always satisfied regardless of profit and cost considerations. Patinkin (1965), 33 Solow and Stiglitz (1967), 34 and Barro and Grossman (1971) 35 have pointed

8a D. Patinkin, Money, Interest, and Prices, second edition, New York etc., 1965, Chapter 12.

~4 R. M. Solow and J. E. Stiglitz, 'Output, Employment, and Wages in the Short Run,' Quarterly Journal o/Economics, L X X X I I (1968), pp. 537-560.

35 R. J. Barro and It. I. Grossman, 'A General Disequilibrium Model of Income and Employment, ' American Economic Review, LXI (1971), pp. 82-93.

572 s.K. KUIPERS

out, however, that there is no reason to expect entrepreneurs to behave in this way under all circumstances. According to these writers, entrepreneurs will only adjust output to demand as long as the real wage rate is less than the marginal physical labour productivity. On the other hand, entrepreneurs may well desire to ex- pand output in order to bring about an equality between these variables, but the level of effective demand may make this im- possible for them. Production is a demand-constrained process.

The situation is different, however, if satisfaction of total demand for produced goods implies that the marginal labour productivity will be less than the real wage rate. Profit maximizing entrepreneurs will not accept such a situation. Production will be lowered until the equality between the marginal labour productivity and the real wage rate is restored. Output is restricted by effective supply. Excess supply in the labour market coincides with excess demand in the market of produced goods.

The idea that output may be restricted by effective demand as well as by effective supply is important. However, it is question- able whether the supply constraint is really determined by the equality between the real wage rate and the marginal physical productivity of labour. This presupposes that an entrepreneur has all the information and knowledge about the present (market trans- parency) as well as about the future (per/ect/oresight) necessary to be able to calculate an optimal solution. This may be true in a stationary economy, but in an uncertain and rapidly changing world it is not. In reality an entrepreneur is not in a position to calculate optimal solutions for the simple reason that he does not have enough knowledge to determine what is optimal. In reality de- cision procedures take place in a much more primitive way. As his information about the present and the future is very limited, the entrepreneur is forced to use simple criteria to judge the extent to which his results are 'good' and to decide whether new measures must be taken.

For these reasons the idea that the equality between the real wage rate and the marginal physical labour productivity should be the supply constraint is rejected in the present study. It will be assumed instead that when the entrepreneur considers satisfying demand, he compares the real profit margin q~ with a certain critical value qc. The entrepreneur regards the value at which the survival of the firm is jeopardized as the critical value of the profit margin.

A DEMAND AND S U P P L Y MODEL OF ECONOMIC GROWTH 573

To prevent this danger, he will t ry to ration labour by reorganizing the production process when qt has fallen below qe, which in technical terms implies a reconstruction of existing machinery and a lowering of the running speed of machines. In this way the labour intensity of the production process will decrease, and within the substitution interval this will entail a rise in average labour productivity. At a given real wage rate this implies a rise in the profit margin.

It follows from the argument given above that entrepreneurs will react to a fall of the profit margin below qe by decreasing the labour intensity or, what comes to the same thing, by decreasing the average capital productivity. The supply equation may then be written a s

x t = i (q t ) , i ' (q t ) > O. (3.2.8)

An extreme case occurs when entrepreneurs change the labour intensity in such a way as to exactly maintain the critical value of the profit margin. The supply curve is then a vertical straight line.

This adjustment process of substituting capital for labour may go on until the boundary of the substitution interval has been reached. With reference to Figure 3.2.2 this means that capital is substi- tuted for labour until the labour intensity nt has become equal to n*. For nt < n* a decrease in the labour-capital ratio will cause the average labour productivity to fall, and consequently the profit margin will decrease at a given real wage rate. Thus there is no rationale for lowering nt below n* and xt below x*. Hence, for values of qt below q* - the value corresponding to x* according to supply equation (3.2.8) - the supply equation is

act ~- x*. (3.2.9)

If in this range the demand for goods per unit of capital is an increasing function of the profit margin, then there may be some qt,

say qt = q**, for which the equality between demand and supply is restored. For qt < q** output is restricted by effective demand. Output will be adjusted to effective demand by reducing the number of operating hours per machine or by putting machines out of use. In this way the ratio of output to capital i n use remains equal to x*, while the ratio of output to capital on h a n d decreases, ad- justing itself to the ratio of demand to capital on hand.

It is now time to put the pieces of the jigsaw puzzle together.

574 s.K. KUIPERS

(1) In the interval 1 >__ qt > qc, output is determined by effective demand"

X t = Yr. (3.1.16)

(2) In the interval qc > qt > q*, output is determined by effective supply according to equation (3.2.8)"

= > o. (3 .2 .8)

(3) In the interval q* > qt > q**, output is determined according to equation (3.2.9):

xt = x*. (3.2.9)

(4) In the interval q** > qt > O, output is determined by effective demand:

X t = Yr. (3.1.16)

The output curve is sketched in Figure 3.2.3. With respect to the demand curve only the stable part ABDEF is presented. The curve

x t

XI~OJ(

X~I__

q ~ q~" qe

E D

F

q

Figure 3.2.3 qt


CD is the supply curve corresponding to equation (3.2.8); the line BC is the supply curve corresponding to equation (3.2.9). As dis- cussed above, the market of produced goods is in excess demand at all points below the semioval ABDEF. Hence, on the supply curve BCD the commodity market is in excess demand.

3.2.3 T h e W a g e a n d P r i c e E q u a t i o n s

In the neo-classical theory the wage rate and the profit rate are explained by the productivity theory. Taking perfect competition (Joan Robinson) and profit maximization for granted, we can say that the real wage rate and the profit rate are equal to the marginal productivity of labour and capital respectively. Income distribution is fully determined by the characteristics of the production structure and the available quantities of capital and labour. In this theory there is no room for institutional factors.

As indicated above, the assumption of profit maximization is not realistic in a rapidly changing world. Moreover, wages and prices are not determined under perfectly competitive conditions. In most Western countries the money wage rate results from a collective bargaining process. Its level depends on the bargaining positions of workers' and entrepreneurs' organizations as well as on the ob- jectives of both market parties.

To explain the level of the money wage rate in a situation of bilateral monopoly, Pen's wage theory will be taken as the point of departure. 36 According to Pen, the development of the money wage rate is determined by two factors:

(1) the situation in the labour market, measured by the rate of unemployment;

(2) the criterion used in the bargaining process, this criterion being the labour share of the national income. The labour share, zt,

is defined as

W ~ N ~ zt - , (3.2. l 0)

P t X t

where W t is the money wage rate and P t is the price level.

a6 j . Pen, 'De determinanten vail de inkomensverdeling: een formule ten behoeve van de praktijk,' De Economist, CIII (1955), pp. 685-707; J. Pen, 'Versehraling en over- verzadiging in de loontheorie,' De Economist, CV (1957), pp. 737-753; J. Pen, Modern Economics, Penguin Books, 1965, p. 184.

576 s.K. KUIPERS

Equation (3.2.10) may be rewritten as

W~ zt -- (3.2.11)

X t P t - -

N t

According to equation (3.2.11) the money wage rate depends on the price level and on the average labour productivity at a given value of the labour share. Hence, the determinants of the money wage rate are"

(1) the rate of unemployment, ut;

(2) the price level, Pt; X t

(3) the average labour productivity, N t

Based on econometric research the following functional relationship is plausible"

cot - - G(~zt, cq ut) G ~ > 0 ; G ~ > 0 ; Gu < O. (3.2.12)

In this equation cot denotes the growth rate of the money wage rate, ~t is the relative rise in the price level, ut symbolizes the rate of unemployment, and ~ represents the steady state rate of growth of labour productivity. The latter growth rate is equal to the rate of labour-augmenting technical progress. 37

Furthermore, d W t

dt cot -- , (3.2.13)

W t

dPt

dt ~ t - - , ( 3 . 2 . 1 4 )

Pt

N t - - N t ut -- -~t (3.2.15)

In the last equation Nt is the working population. The origin of the wage equation (3.2.12) lies in the research done

by Phillips regarding the relation between the relative change in

a7 A c c o r d i n g to Solow a n d St igl i tz , i t is n o t so m u c h the a c t u a l g r o w t h r a t e of l a b o u r p r o d u c t i v i t y as the t r e n d g r o w t h r a t e w h i c h in f luences the g r o w t h r a t e of t he m o n e y w a g e r a t e . Solow a n d St ig l i tz (1968), pp . 543-545 .


o 3 t

F i g u r e 3 .2 .4 ut

the money wage rate and the rate of unemployment, as The graphi- cal representation of this relation is known as the Phillips curve. This relation is sketched in Figure 3.2.4.

Figure 3.2.4 shows a trade-off between the relative change of the money wage rate and the rate of unemployment. A choice must be made between a rise in the money wage rate and the resulting inflation on the one hand and unemployment on the other. Inflation, then, will not present itself if an unemployment rate u~ = u* is ac- cepted. 89

Later empirical research revealed the Phillips curve to be unstable. The unstability, however, can be removed by including more variables in the wage equation. 40 The results of these investigations are reflected in the wage equation (3.2.12).

3s A. W. Phillips, 'The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957/ Economics, N.5., XXV (1958), pp. 283-299.

~9 This view is in conflict with tha t of a group of American economists (e.g. Phelps (1967, I970) and Friedman (1970)) tha t denies the existence of the trade-off. They hold the view that , if the mat te r is examined over a period longer than the short run, the rate of unemployment is independent of the rate of inflation - they believe tha t a natural rate of unemployment exists. E. S. Phelps, ' "Phi l l ips Curves", Expecta t ions of In- flation and Optimal Unemployment over Time,' Economics, N.S., X X X I V (1967), pp. 254-281 ; E. S. Phelps, 'Money Wage Dynamics and Labour Market Equil ibrium, ' Micro- economic Foundafions o] Employment and Inflation Theory, E. S. Phelps ed., London, 1970, pp. 124-166; M. Friedman, 'The Role of Molletary Policy,' American Economic Re- view, LVII I (1968), pp. 1-17, esp. p. 8.

4o See, e.g. Van den Beld (I967), p. 24; E. Kuh, 'A Product iv i ty Theory of Wage Levels - An Alternat ive to the Phillips Curve,' Review o/ Economic Studies, X X X I V (1967), pp. 333-360.

578 S.K. K U I P E R S

With respect to the firm's price policy, the mark-up hypothesis that is derived from the theory of full and normal cost pricing will be taken as the point of departure. 41 Entrepreneurs are assumed to pursue a certain profit margin at a desired utilization rate of capital.

The profit margin is defined as

i.e.,

Qt qt - - X t ; (3.2.16)

W t q t = 1

X t P t - -

N t

(3.2.17)

From equation (3.2.17) it follows that, at a given profit margin, the price level depends on the money wage rate and on the average labour productivity. If it is assumed that price policy is based on a desired utilization rate of capital, only the trend value of labour productivity is relevant in price setting.

The actual and the desired utilization rates of capital (0t and v~ respectively) are defined by

Xt ~ t - - , ( 3 . 2 . 1 8 )

Xmax

Xd v% -- (3.2.19)

Xmax

In equation (3.2.19) x~ is the desired value of average capital productivity. If 0h is a constant, x , is a constant too. Hence, pr ice setting under the condition of a desired utilization rate of capital implies doing it at a given value of average capital productivity. According to the production equation (3.2.7) average labour productivity at a given capital productivity x~ increases with the rate of labour-augmenting technical progress. By assuming this growth rate to be constant and equal to ~, it may be concluded that the relevant labour productivity variable in price setting is the steady state variable growing at a constant growth rate ~.

Price setting will not be independent of the situation in the commodity market. A situation of excess demand will lead to a rise in

~1 For a survey of these theories see, e.g., J. E. Andriessen, De ontwikkeling van de moderne prijstheorie, third edition, Leyden, 1965, Chapter VII.


the price level; a situation of excess supply to a fall. Thus the determinants of the price level are:

(1) the money wage rate; (2) the level of labour productivity at the desired utilization rate

of capital, (3) the disequilibrium situation on the market of produced goods.

The following functional relationship is plausible42:

~t = J(cot, oL, gt) J~ > o, J~ < 0, Jg > 0. (3.2.20)

In this equation gt is the relative excess demand in the market of produced goods; i.e.,

Y t - - X t (3.2.21) gt - - X t

In this article linear specifications of the wage and price equations will be applied. Therefore,

cot = 21:~t + 22~ - - 2aut + co*,

0 " ( ,~1 "( 1; 42 > 0; ha > 0 ; (3.2.22)

zct = #lcot - - #2o~ + #agt + zc*,

0 ~/~1 < 1; /z2 > 0; /*3 > 0. (3.2.23)

In these equations it is assumed that a lag exists in the adjustment of wages to prices and vice versa:

(3.2.24) 0 < # 1 < 1.

The real wage per unit of labour in efficiency units, wt, increases at a rate of

z0t - - cot -- ~t -- ~. (3.2.25)

wt

From equations (3.2.22) and (3.2.23) this growth rate can be expressed as

4~ See, e.g., Van den Beld (1967), p. 24.

5 8 0 s . K, K U I P E R S

Z0t ~2(1 - - if1) @ if2( 1 - - ~1) @ ~I/A1 - - 1

W t 1 - - 11~1 ff (i - &)

gt I - - AI/~I

x 3 ( 1 - f f l ) ~ t

1 - - ~ l f f z

1 - - > 1 q- ~o*

1 - - Xl/A1 I -- AI - - =*. (3.2.26)

1 - - ~ 1 f f l

Since 0 < 41 < 1 and 0 < ¢1 < 1, an increase in the unemployment rate and in the relative excess demand in the commodity market will bring about a decrease in the growth rate of the real wage per unit of labour in efficiency units. An increase in the trend growth rate of average labour productivity may exert either a negative or a positive influence.

3.2.4 L a b o u r S u p p l y , I n c r e a s e in t h e S t o c k of C a p i t a l , a n d T e c h n i c a l P r o g r e s s

The working population will be assumed to grow at an autonomous and constant rate:

Nt = 3F0 exp (St). (3.2.27)

The same will be assumed with respect to technical progress"

At = A0 exp (st). (3.2.28)

Depreciation of capital goods will be assumed to be nil - capital lasts forever. Real investment leads to an immediate increase in the stock of capital; i.e.,

dKt z t - (3.2.29)

dt

Equation (3.2.29) holds true not only in a situation in which the market of produced goods is in equilibrium but also in a situation of excess demand. Since entrepreneurs, in contrast to consumers, have easy access to bank credit, they are able to realize their in-

A D E M A N D A N D S U P P L Y M O D E L OF E C O N O M I C G R O W T H 5 8 1

tended increase in the stock of capital. The excess demand in the market of produced goods is shifted to consumers. Due to the consequent inflation, consumers are not in a position to realize their intended real consumption expenditures (forced savings). 43

3.3 The Demand and Supply Model

It is now possible to formulate the complete model. Demand model

Y t = Ct + It (3.1.1)

Ct = Zt 4- c2Qt, 0 ~ ca < 1 (3.1.2)

Zt -j- Ot = X t ( 3 . 1 . 4 )

I t - - i l KT-Th(qt , m ) - - i 2 K t , O < v < 1 i 1 . ' > 0 ; i 2 ~ 0 (3.1.14)

h ¢ > 0

hq¢ < 0 (3.1.15)

h m > 0

h = 0 for q t = 0

9 , (3.2.16) q t - X t

Supply model X t = F(AtNt , Kt) (3.2.7)

F2v > 0 and FK > 0 iff n*<-- Nt - - <= nrr~ax (3.2.2) ~ _ _ I ~ t

F~yN < 0 I (3.2.3) FKK .~ 0 J

At = Ao exp (st) (3.2.28)

dKt - Zt (3.2.29)

dt

Xt =- Y t if 1 >= qt >= qc or q** > qt > 0 (3.1.16)

xt = i(qt) if qe >- qt > q* i ' (qt) > 0 (3.2.8)

xt = x* if q* >= qt >~ q** (3.2.9)

4a Only in the shor t r un is i t possible to sa t i s fy consumer d e m a n d ou t of i nven to r i e s ; th is poss ib i l i ty does no t ex is t in the i n t e r m e d i a t e run.

582 S. K. KUIPERS

Xt xt - - (3.3.1)

K t

(3.2.22)

¢ t t : f f l tOt - - ff2o~ -~- #3gt -~- ¢t*, (3.2.23)

d W t

dt (~t -- W t (3.2.13)

dPt

dt ~t -- (3.2.14)

Pt

N t - - N t ut - - N t (3.2.15)

Yt - - X t gt - - X t (3.2.21)

W t Zt = - - N t (3.3.2)

Pt

-N, ---- N0 exp (~t) (3.2.27)

The model consists of 18 equat ions in the 18 unknown variables At, Ct, gt, I t , Kt , Nt , Nt , Pt, Qt, qt, ut, v~t, x t , xt, Y t , z t , 7~t, e)t.

4 THE WORKING OF THE MODEL IN THE SHORT RUN

In the short period the capital s tock is constant :

K t = / ~ . (4.1)

For simplicity the labour force and the s ta te of arts will also be assumed to be constant :

Nt = ~'Y, (4.2)

A t = 1. (4.3)


Equations (3.1.18), (3.2.8) and (3.2.9) describing the output curve depicted in Figure 3.2.3, may be rewritten as

il s2qt = RT-_l X~-lta(qt, m) - - i2 I7~

X t ' (4.4)

1 >--q t~qc , q * * ~ q t > 0;

X t = i (qt )R, q~ > qt > q*; (4.5)

X t - - x*_K, q* ~ qt ~ q**. (4.6)

Equations (4.4)-(4.6) describe a relation between the output and the profit margin.

According to equation (3.2.26), the short run real wage equation is

ze'~t - - fl2gt - - f l3¢t t @ f14, /32 > 0, /ga > 0, (4.7)

w t

in which

and

- - 23(1 - - / * i ) /32- /*a(1 21) f l a - - 1 - - k l / * i ' 1 - - 2 1 / , 1

1 - - / * 1 1 - - 21 ~ 4 - - 09 ~ * .

1 -- kl#i 1 -- ki#i

Y t -- X t The relative excess demand, g t - -

I t - - S t X t gt - - - - it - - st.

X t ,~ - - N t The unemployment rate is equal to ut =

N the production equation it is also possible to write

F - I ( N t , K ) u t = 1 _F

, can be rewritten as

• According to

Substitution of these relations into equation (4.7) gives

~'t _ /~(it - st) -4- /3~ F-~(Xt, ~) + P4 -/~a. (4.8) wt

Since A t -~ 1, the real wage per unit of labour in efficiency units wt

is also equal to the real wage per unit of labour in natural units, i.e., the real wage rate.

584 S. K. KUIPERS

When the real wage rate is constant, equation (4.8) reduces to

0 = --fig.(it -- st) q_ -=-_f13 F_I (Xt ' ~) q_ f14 -- fla. (4.9) N

Because it is a function of X t and qt and because st is a function of only qt, this equation is the second relation between Xt and qt. The curve of Xt as a function of qt will be indicated as the 'wage

dXt curve'; its slope, ~q~ , is equal to

Sit $ 2 - - - -

dXt ~qt dqt -- Sit dF- l (X t , I~) fi~ (4.10)

~Xt dXt fll ~.

~it - - will be assumed to be In the same way as for Figure 3.2.3, OXt

negative. (This is a necessary condition for a stable commodity market.) On the strength of the comments made in section 3.1 it

3it Sit holds true that s2 < - - for qt < q and that s2 > - - for qt > q.

~qt 3qt dF- l (X t , K)

Furthermore, since > 0, equations (4.4) and (4.9) dXt

have a maximum value of Xt for the same value of qt; namely, qt = q. Because the denominator of equation (4. I0) is greater in absolute value than that of equation (3.1.19), the derivative (4.10) is in absolute value less than the absolute value of the derivative (3.1.19). Hence, the slope of the wage curve is less than that of the output curve.

The output curve and the wage curve are sketched in Figures 4.1- 4.4. For the sake of brevity, attention will be paid only to cases in which Xt > X*. For the post-war situation, with lasting inflation and with only minor depressions, these cases are the most inter- esting ones. In these diagrams Xmax is the maximum output at- tainable with the given capital stock. It is assumed that the full- employment level of output, Xmax, is always less than this technical maximum. Thus, unemployment due to capital shortage will not arise. This is likely to be true in Western countries44; in the underdeveloped countries this is not so.

44 See a l so K a l d o r (1961) , p p . 197-198 .


X ~

T1

A

T5

Xt

Xmax

X max

~ W

qt Figure 4. i

Xt Xmax Xmax

X ~

E

u r2~, . - i I i \

g

0 Figure 4.2

W

qt

In the diagrams 4.1 and 4.2, the output curve ABCDEF lies below the full employment line. In the diagrams 4.3 and 4.4 the output curve ABCDEF and the full employment output line have two points of intersection, H1 and H2. Since output cannot exceed its full employment level, the curve relating actually producible output to the profit margin is in these cases ABCD HIH2F.

586 S. K. KUIPERS

X rna E

// IV ", X'moxL H1 / ~ ~ Q ' 3 S 2 T2"-{ $3~H2

u I; I w x* . . . . . B~..J c

I A

Figure 4,3

r

qt

E

X ma.~

D

X* ---- U S 4 t ~ ¢ 1 "*~

A

Figure 4.4

~ W

l i . . _ r

qt


The curve UVW is the wage curve. In the diagrams 4.1 and 4.2, this curve and the output curve have two points of intersection, S1 and $2. In figure 4.1, both S1 and Se, are points on the demand- restricted part of the output curve. Since the level of output in S1 and $2 is less than Xma•, employment is not full so that a tendency towards full employment does not occur. The output level, the distributive shares and the unemployment rate are determined by demand as well as b y supply factors. To bring about full employment, discretionary policy measures leading to a rise in the output and wage curves are necessary.

In Figure 4.2, $2 is a demand-restricted point, but $1 is a supply- restricted point of the output curve. Output, distributive shares, and unemployment are in this case primarily (but not completely) determined by supply factors; the market of produced goods is in excess demand.

Diagrams 4.3 and 4.4 show four points of intersection: S1, $2, Sa, and $4. In Figure 4.3, $1 and $4 are demand-restricted points of the output curve, while at $2 and Sa output is restricted by the size of the working population. Figure 4.4 differs from Figure 4.3 in that S1 is not a demand - but rather a supply-restricted point of the output curve. At points S1, $2, and $3 of Figure 4.4 output and distributive shares are primarily (but not exclusively) determined by supply factors; and at $4 they are determined by supply as well as by demand factors. In both diagrams 4.3 and 4.4, the market of produced goods is in excess demand at $2 and Sa.

On the strength of the above, it may be concluded that at the points of intersection of the output curve and the wage curve, the level of output and the distribution of income are constant. The market of produced goods and the labour market are not necessarily in equilibrium, and lasting situations of unemployment and of excess demand in the commodity market are possible. Moreover, the rate of change of the price level is not necessarily zero. Ac- cording to equations (3.2.22) and (3.2.23), the relative change of the price level is equal t o :

# 1 t 2 - - #2 #a ~12a :~t - - o~ + gt u t +

1 1 + ~* + - o~*. (4.11)

588 S . K . K U I P E R S

By recalling that ~ = 0, equation (4.11) may be written as

#3 #12a 1 m - gt ut + ~* +

1 - - l t l / t l 1 - - } L I # I 1 - - J t l / * l

+ ~ ~*. (4.12) 1 - - 21#1

This equation shows that the rate of inflation depends on the relative excess demand in the market of produced goods, on the unemployment rate; and on the autonomous relative wage and price increases, ~* and x*. There is no reason for ~, to be equal to zero. Since the level of output and the profit margin are constant at the points of intersection of the output curve and the wage curve, the relative excess demand in the commodity market and the unemployment rate are also constant. Hence, at these points of intersection the price level increases at a constant rate. And, since the real wage rate is constant, the money wage rate also increases at a constant rate.

Before concluding this section it is necessary to investigate the stability properties of the model at the points of intersection. As has been pointed out in section 3.1, the market of produced goods is in excess demand at points under the demand-restricted parts of the output curve and in excess supply at points above these parts. This means that output will rise at points under and fall at points above those demand-restricted parts of the output curve. I t is plausible that the same will happen at points under and above the supply-restricted part of the output curve. Hence, Xt will rise from points under the curve ABCDEF and fall from points above this curve. From equation (4.8) it can be shown that at points under the wage curve the real wage rate will decrease, whereas at points above this curve it will increase.

Point T1 in Figures 4.1 and 4.2 lies above the output curve as well as above the wage curve. The commodity market is in excess supply and hence output will fall. Since Xmax > Xt > X*, a fall in output implies a fall in average physical labour cost, and this will have a positive effect on the profit margin. The rise in the real wage rate, however, exerts an opposite effect on the profit margin. Thus the ultimate direction of the change in the profit margin is not unambiguous. To remove this ambiguity the question which must be answered is that of which adjustment is most important

A D E M A N D AND S U P P L Y M ODE L OF ECONOMIC G R O W T H 5 8 9

in the short run - the quanti ty adjustment or the price adjustment. Keynes (1930, 1936) was of the opinion that the adjustment velocity of factor prices to disequilibrium situations is much lower than the adjustment velocity of flows of goods. 45 In the short run the latter completely overshadows the former. 46 The present author be- lieves this to be a very realistic adjustment hypothesis. This means that it may be assumed that the positive effect on the profit margin of a fall in average physical labour cost is greater than the negative effect of a rise in the real wages. As a result of these opposite forces, the profit margin will rise.

In the same way the direction of the arrows at the other points in Figures 4.1 and 4.2 can be established. It turns out that the points $1 in both figures are stable and the points S~ are unstable.

In Figures 4.3 and 4.4, there are four points if intersection: two full employment points ($2 and $3) and two underemployment points ($1 and $4). Along the same lines as in the preceding paragraphs, it can be established that the underemployment points S1 are stable and the underemployment points $4 unstable. The full employment points $2 are unstable and the full employment points $3 are stable. In economic situations that are represented by one of the points T1, a rise in the real wage rate will occur causing the profit margin to shrink because the average physical labour cost is constant with full employment prevailing. Until the point HI is reached, the wage rate rises while full employment is maintained and the commodity market is in excess demand. At point HI there is neither excess demand nor excess supply in the market of produced goods. When H1 has been passed, the market of produced goods has reached a situation of excess supply and output will fall. The economy tends to point $1. In the same way it can be proved that, starting from points T2 and T~, the economy tends to S~. So there exists one stable full employment intersection point and one stable underemployment intersection point.

As stated earlier, it is assumed that adjustments of flows of goods are much faster than price adjustments. It has, none the

45 j . M. Keynes, A Treatise on Money, Vol. I, London, 1930; J. M. Keynes, The General Theory o] Employment, Interest and Money, London, 1936.

as According to Leijonhufvud (1967, 1968) Keynes reversed Marshall 's ranking of price-and-flow ad jus tment velocities. A. Leijonhufvud, 'Keynes and the Keynesians: A Suggested Interpretat ion, ' American Economic Review, Papers and Proceedings, LVII (1967), pp. 401-410, esp. pp. 402-404; A. Leijonhufvnd, On Keynesian Economics and the Economics o/ Keynes, New York, etc., 1968, esp. Chapter II.

590 s.K. KUIPERS

less, been assumed that price adjustments, although slower than quanti ty adjustments, can be completed within the short period. This assumption is not at all realistic. 4v According to Keynes, the adjustment velocity of prices will be so low as not only to be over- shadowed by the adjustment velocity of flows of goods but also to make the process of price adjustment incomplete within the short period. 4s This implies that the intermediate period is characterized not only by a growing stock of capital but also by changing prices and by the disequilibrium situations that go with them. 49

Due to the relatively low adjustment speed of prices, these dis- equilibra do not disappear within the intermediate period. Ac- cording to the terminology introduced in section 1, these disequilibria must be denoted as 'lasting disequilibria.' Since lasting disequilibria are basic characteristics of the intermediate period, it is necessary in an intermediate period study to pay attention to the causes and consequences of a growing capital stock and to those of changing prices as well. The flow adjustments may be assumed to be completed within the short period. Because the flow adjustments may be assumed to be completed within the short period, the economy may be considered in an intermediate period study to be on the output curve.

5 THE PROCESS OF STEADY GROWTH

As pointed out in the last paragraphs of section 4, economic development in the intermediate period is characterized not only by a changing capital stock but also by disequilibrium situations due to the low adjustment speed of prices. Quantity adjustments are so fast that they may be considered to be completed within the short period, and this implies that the economy is in a position of output equilibrium (i.e., it is on the output curve) in the intermediate period.

The growth model of section 3 exhibits the following characteristics: the economy is on the output curve, the capital stock is growing, the labour market and the market of produced goods are not necessarily in equilibrium, and changing prices and wages are possible. This model may be reduced to the following set of equa-

47 Since Solow a n d St ig l i tz (1968) also a s s u m e d pr ice a d j u s t m e n t s to h a v e c o m e to a n e n d in t he s h o r t r u n , th i s c r i t i c i sm also appl ies to t he i r armlysis .

43 K e y n e s (1930), p. 207. 49 See also Wi l l i amson (1970), pp . 157 a n d 158.


tions: 1

s2qt=ilx~-lh(qt , m ) - - i 2 - , I>=qt>=qc, q**>=qt>O; (3.1.18) x t

xt -- j(qt), qc >= qt >= q*; (3.2.8)

xt = x*, q* >= qt ~ q**; (3.2.9)

xt =/(et); (5.1) zOt

- - f l l O~ - - f l 2 g t - - f i 3 U t @ f14. (5.2) W t

The first three equations are the output equations. Equation (5.1) is the production equation; it is derived from equation (3.2.7) by dividing the left and the right hand terms by Kt and by setting AtNt

- - equal to et. In equation (5.2), wt denotes the real wage per Kt

unit of labour in efficiency units. This equation is derived from equation (3.2.26) by setting the parameters a, gt, and ut and the constant equal to t31, fi2, f13 and f14 respectively.

The unemployment rate ut may be written as

Nt A tNt u ~ = l - -1

-~t A tNt

E t

Et Kt et = I Et --1 Et --1----& (5.3)

Kt

Here Et stands for the employment of labour in efficiency units, ~'t represents the supply of labour in efficiency units, et denotes the employment of labour in efficiency units per unit of capital, and & symbolizes the supply of labour in efficiency units per unit of capital.

F rom equation (5.1), equation (5.3) may be rewritten as

/-l(x~) u t - 1 (5.4)

~t

In this section the steady state properties of the growth model will be examined. A process of steady growth may be defined as the process in which variables like output , capital stock, and em-

592 s.K. KUIPERS

ployment in efficiency units are growing at the same rate as the supply of labour in efficienty units. This latter growth rate is denoted by g and is equal to

e = ~ + ~ . (5.5)

The consequence of output, capital, and employment and supply of labour in efficiency units growing at the same rate g is that the average capital productivity (xt), the effective labour-capital ratio (et), and the supply of labour in efficiency units per unit of capital (gt) are constant. If, for the sake of brevity, the analysis is again restricted to xt > x*, it may be concluded from equations (3.1.18) and (3.2.8) that the distributive shares are also constant. Since average labour productivity is growing at a constant rate ~, the real wage rate must also grow at this same rate. Hence, the real wage per unit of labour in efficiency units is constant; i.e.,

z0t - o. (5.6)

w t

It follows that in a state of steady growth equation (5.2) reduces to

0 =- ~10~ - - f i2gt - - /~3Ut + ~41 (5.7)

Since ~t is a constant and since gt is a function of only xt and qt,

equation (5.7) defines a stable relation between xt and qt. Re- placing X t by xt we see that this relation has the same properties as the relation defined by equation (4.9). The second relation between xt and qt is defined by the output equations (3.1.18), (3.2.8), and (3.2.9). The behaviour of the output curve has already been derived in section 3 and illustrated in Figure 3.2.3.

Both the wage curve and the output curve are sketched in Figures 5.1-5.4. In these figures ABCDEF is again the output curve and UVW the wage curve. The symbols xm~x and 2max represent the technically maximal capital productivity and the capital productivity at full employment respectively. Since technical progress is only labour-augmenting, Xma x is a constant. In a steady growth situation 2max is also a constant.

In Figures 5.1 and 5.2, the points S1 and S~ are the points of intersection of the output curve and the wage curve. Because $2 turned out to be unstable in the short run, only $1 will be considered as a relevant point. In Figure 5.1 S1 is a point of the demand-restricted part of the output curve. This means that the

A D E M A N D AND S U P P L Y MODEL OF ECONOMIC GROWTH 593

xt

XmQ)

XmGX

X ~

0

E

/ A F

q qt

F i g u r e 5.1

xt

X mo;

mcIx

X ~

//

A I \F t

# qt

F i g u r e 5 .2

594 S. K. K U I P E R S

xt

XI'BOX

m O X

X ~

E

H1. ~ ",,H2

51 52 S W

U Ill

---~C A F

F i g u r e 5 .3

qt

x t

XmGx

XmOX

X ~

H~/ . f ~ T " - - ~ H2

U / / !

/ W / -----y

A F

q

F i g u r e 5 .4

qt

A D E M A N D AND S U P P L Y MODEL OF ECONOMIC G R O W T H 5 9 5

average capital productivity, the profit margin, and therefore the income distribution are determined by demand as well as by supply factors. The same holds true for the unemployment r a t e - both the output curve and the wage curve are below the 2max line.

In Figure 5.2 the steady state wage curve intersects the output curve in the supply-restricted part. Thus income distribution as well as average capital productivity are primarily (but not exclusively) determined by supply ~actors. To diminish unemployment, deliberate policy measures must be taken primarily on the supply side.

Figures 5.3 and 5.4 show four points of intersection: $1, $2, $8, and $4. As $4 is an unstable point in the short run analysis, only $1, $2, and $3 will be considered as relevant points. Although in the brief analysis of the foregoing section $2 also turned out to be unstable, this point will be further examined in t he next section because the unstabil i ty is due not to output adjustments but rather to wage adjustments, the latter being more intermediate than short- run phenomena as has been explained above.

The points $2 and S~ are full employment points. Steady growth at those points is not balanced, however: the market of produced goods is in excess demand. Income distribution and average capital productivity are primarily (but not exclusively) determined by supply factors.

In Figure 5.3 the point of intersection $1 is a point of the demand- restricted part of the output curve. Hence, average capital produc- t ivi ty and income distribution are determined by both demand and supply factors. In Figure 5.4 $1 is a point of the supply-restricted part of the output curve. Hence, the average capital productivity, the unemployment rate, and the income distribution are primarily (but not exclusively) determined by supply factors. Unemployment in the labour market goes together with excess demand in the market of produced goods. To obtain equilibrium growth deliberate policy measures must primarily be taken on the supply side~

It may now be concluded that a process of steady growth is not necessarily balanced - the market of produced goods may be in excess demand and the labour market may be in excess supply. Be- cause the wage per unit of labour in efficiency units shows no tendency to change at the points of intersection of the wage curve and the output curve, these disequilibria are everlasting. Moreover, there is no reason for the price level to be constant. According to equation

596 s. K. KUIPERS

(4.11) the rate of inflation depends on the growth rate of average labour productivity, on the degree of excess demand for produced goods, on the rate of unemployment , and on the autonomous relative price and wage increase.

6 THE STABILITY OF THE STEADY STATE GROWTH

In this section the local stability properties of the steady state growth will be investigated. This will be done for the following three cases treated in succession:

(1) output is restricted by effective demand, (2) output is restricted by effective supply, (3) output is restricted by size of the labour force.

6.1 Output is Restricted by E//ective Demand

The non-steady state model in the demand-restricted case consists of the following equations:

s2q t=i l x~- lh (q t , m) - - i 2 - - 1

1 ~ qt > qc; Xt '

zOt

Wt - ~ 1 ~ - p ~ u t + 8 4 ;

/-l(x,) ut----- 1

dt

q~ = 1 - w t l ( x t ) , Z'(x~) > 0;

~t

~t -- g -- ilx~h(qt, m) + i2.

(3.1.18)

(6.1.1)

(5.4)

(6.1.2)

(6.1.3)

Equation (3.1.18) is the demand-restricted output equation. The interval q** > qt > 0 is again ignored. The wage equation (6.1.1) has been derived from equation (5.2) by setting gt equal to zero (the market of produced goods is in equilibrium in the demand- restricted case).

Equat ion (6.1.2) is a rewritten form of the definition equation of the profit margin; i.e.,


w t A t N t w t E t qt = 1 X t - - 1 X t

et / - l ( x t ) 1 - - W t - - ~ 1 - - W t - -

Xt Xt

= 1 - - w t l ( x t ) . (6.1.2)

In the relevant interval, x* < xt < Xmax, average effective labour productivity decreases if xt increases; i.e. if l '(xt) > O.

Equation (6.1.3) can be derived as follows.

Et e t - ( 6 . 1 . 4 )

K t

Taking natural logarithms of both terms of the equation, one obtains

log et ----- log Et -- log K t . (6.1.5)

Differentiation with respect to t yields

~t - g - ~t. ( 6 . 1 . 6 )

&

According to equation (3.1.14) one may write

~t - - g - - i lx~h(qt, m) + i2. (6.1.3)

&

To investigate the local stability properties, all equations of the model will be linearized in the environment of the steady state value of the variables. It is therefore convenient to switch to another notation.

Because gt = it - - st, equation (3.1.18) may be written as

Sit Since - - &t ~Xt

- - O, 3xt

g(xt, qt) = O. (6.1.7)

has been assumed to be always negative and since

~g gx -- < 0. (6.1.8)

~xt

With only points on the increasing part of the output curve being

598 S. K. KUIPERS

relevant, we m a y write (based on the s ta tements made in section 4)

i.e.,

~it s~ ~ - - ;

Oqt

~g gQ -- > O. (6.1.9)

aqt

From equations (6.1.1) and (5.4) follows

w~ /-*(*t) - / h o ~ +/~a - - +/~4 - /3a . (6. t. l o)

wt gt

This equation m a y be rewrit ten as

wt - - b(xt, at). (6.1.11)

wt

Since/--l'(xt) ~> 0 and fla > 0, it holds true tha t

~b b, -- > O, (6.1.12)

c~xt

~b b e -- < O. (6.1.13)

Equat ion (6.1.2) m a y be rewrit ten as

qt = a(wt , xt) . (6.1.14)

With l ' (xt) > 0, one m a y write

6q6~ aw - - < O, (6.1.15)

~w

ax -- < O. (6.1.16) 8x

Finally, equation (6.1.3) m a y be rewrit ten as:

~t -- k(xt, qt). (6.1.17)

gt

A D E M A N D A N D S U P P L Y M O D E L O F E C O N O M I C G R O W T H 599

By virtue of 0 < v < 1 and h ' (q t ) > O,

8k ka: - - < 0 , (6.1.18)

&t

8k k q - - < O. (6.1.19)

8qt

Linearization of equations (6.1.7), (6. I. 11), (6. t. 14), and (6.1.17) gives

g~(x t - - x s) -t- gq(qt - - qs) = O, • ( 6 . 1 . 2 0 )

fiat = w s b s ( x t - - x*) @ wsbe(gt - - gs), (6.1.21)

qt - - qS = asw(wt __ ws) @ a s ( x t __ x8), (6.1.22)

& = askg(x t - - xs) + ask~(qt - - U ) . (6.1.23)

In these equations the superscript s means that the variables assume their steady state values.

The model may be solved to yield

81.)8 8 8

f i t = w _xgqaw (wt - - w 8) + wsbe(gt - - gs), (6.1.24) gqa ,

-s s s s "S s s s i t = - - e k x g q a w - - 6 l~qawg x (Wt - - Ws ) . (6.1.25)

g ~ + 8 s g q a x

These equations may be rewritten as

f i t = - A (w t - - ws) - - B ( & - - as), (6.1.26)

i t = C ( w t - - ws) . (6.1.27)

According to the inequalities (6.1.8), (6.1.9), (6.1.12), (6.1.13), (6.1.15), (6.1.16), (6.1.18), and (6.1.19), the constants A, B and C are positive.

The stability of the steady state growth depends on the characteristic roots ,t of the characteristic equation

r C = 0 ;

600 S. K. KUIPERS

i.e., Z ~ + A~ + BC = O, (6.1.28)

- - A ~= a/A 2 4BC 41, 2 = (6.1.29)

2

If A 2 < 4BC, the characteristic roots are complex; if A~ > 4BC, the roots are real. If the roots are complex, the real parts are negative; if the roots are real, they are themselves negative. Hence, the motion is always damped: cyclically damped if A 9' < 4BC, and nonoscillatory damped if A e > 4BC. Thus, the Steady state solution represented by $1 in Figures 5.1 and 5.2 is a stable solution.

The phase diagram of equations (6.1.26) and (6.1.27) is presented in Figure 6.1.1 for the case of A 2 < 4BC. The straight lines AB and CD are the representations of equations (6.1.26) and (6.1.27) for ~0t = 0 and Jt = 0. At the point of intersection S, the economy is in a state of steady growth. Now let us suppose that the economy is in a state of non-steady growth, - say that it is at T. As T lies above AB and CD, wt < 0 and ~t > 0 according to equations (6.1.26) and (6.1.27). The phase diagram shows that the economy is cyclically approaching the point of steady growth S.

w t

W $

T

" - - ~ - 0

I 8 I

~s

D~t =0

• l ,

Figure 6.1.1


6.2 Output is Restricted by Effective Supp ly

Equations (3.1.18) and (6.1.1) are replaced by equation (3.2.8) and (5.2):

xt = i(qt), i '(qt) > O, qe >= qt >= q*; (3.2.8)

~0t - - filc~ -- fl2gt -- fiaut + f14. (5.2)

Wt

According to equation (5.4), equation (5.2) may be transformed to

- - f i l e ~ - - f l 2 g ( x t , q t ) q- fia - - q - / 3 4 - - fla. ( 6 . 2 . 1 ) wt et

For convenience this equation may be rewritten as:

7J2 t -- c(xt, qt, St). (6.2.2)

wt

According to the inequalities (6.1.8), (6.1.9), (6.1.12), and (6.1.13), it is true that:

8c c~ -- > 0, (6.2.3)

8xt

~C c ¢ = - - < 0 , (6.2.4)

8q

~6 c e = ~ - < 0 . (6.2.5)

The model consists of the equations (3.2.8), (6.2.2), (6.1.14), and (6.1.17). Linearization of this model gives

. , _ . s = J a ( ¢ ~ - ¢ ) ,

# t - w~e;(xt - . . ) + w G ( ¢ ~ - ~*) + w%(a~ - as),

q~ - q. = ~ ( w , - ws) + ~**(., - . s ) ,

~t = as]gs(xt - - Xs) -~ dS/eq(qt - - qs) .

(6.2.6)

(6.2.7)

(6.1.22)

(6.1.23)

ai In equation (6.2.6) j q - 3qt

602 s.K. KUIPERS

The above four equations may be solved:

8 8 "8

zOt -- w %{cz]{ + c$} ( m r - wS) -1- wSce(e t - - gs), (6.2.8) 8"8

- - a x ] q

- 8 k 8 "8 8 "8 s 8

Jt = e _ x J q a w -~- e kqa w (wt -- ws). (6.2.9) 1 8"8

- - g x J q


= - - - - - - ( 6 . 2 . 1 0 )

~t = C ( w t - - w s ) . (6.2.11)

According to the inequalities (3.2.8), (6.2.3)-(6.2.5), (6.1.15), (6.1.16), (6.1.18), and (6.1.19), B and C are positive. The sign of A depends on the sign of cdq8., -b %,8" i.e.,

A > 0 if 8.8 Cx] q ~ - - Cq, (6.2.12)

A < 0 if *'* < * cx] q - - Cq.

Along the same lines as in the foregoing subsection, it may be proved that the supply-restricted steady growth is stable if A > 0 and unstable if A < 0.

The reason for the possibility of unstable steady growth is that a rise in the profit margin above its steady growth level brings about a rise in the relative excess demand. Because of this, the real wage rate falls, and the profit margin at constant average labour productivity will tend to rise again. Thus, with average labour productivity constant, a rise in qt above its steady growth level leads to a still faster rise. The only chance to escape this instability is through the rise in xt due to the rise in qt according to the supply equation. For the rise in xt decreases the degree of excess demand in the market of produced goods and decreases the unemployment rate thereby imparting a positive influence on the real wage rate. Moreover, a rise in x~ increases the average physical labour cost. Only if the forces induced by the increase in xt are strong relative to those induced by the rise in qt will steady growth be prevented from being unstable. This will be more likely the steeper is the supply curve xt = / ( q t ) .


6.3 O u t p u t is Res t r i c t ed by the S i z e o~ the L a b o u r Force

In a situation of full employment growth, equation (3.2.8) is replaced by

X t = F(F, t , K t ) ; i .e. ,

x t =/(a t ) , / '(et) > O. (6.3.1)

When full employment prevails, ut = 0. Hence, equation (6.2.1) is replaced by

~d) t - - i l ia - - fl2g(xt, qt) -~ f14. (6.3.2)

wt

Equation (6.3.2) may then be rewritten as

Since gx < O,

~t - - d(x t , qt). (6.3.3)

wt

~d do: -- > O. (6.3.4)

~xt

According to Figures 5.3 and 5.4, gq is positive if qt < 4; further, gq is zero if qt = q and gq is negative if qt > 4- Thus

~d dq -- > --< 0. (6.3.5)

8qt

Linearization of equations (6.3.1) and (6.3.3) yields

8 - x t - - x s -= /e (e t - - eS),

In equation (6.3.6), /e is equal to

(6.3.6)

(6.3.7)

a~ /4 - > o. ( 6 . 3 .8 ) rg&

The solution of the model consisting of the equations (6.3.6), (6.3.7), (6.1.22), and (6.1.23)is

8 8 8 8 8 8 8 dat = w dqaw(wt - - w s) -t- w / e { d q a x + d**}(& - - gs), (6.3.9)

- 8 8 8 8 8 - dt = gskSaS(wtq . - - w s) q- e / e { k x q- kqax}(et - - js). (6.3.10)

604 s.K. KUIPERS


z~t = A (w t - - w s) + B ( g t - gs), (6.3.11)

~t = C(wt - - ws) + D(gt - - gs). (6.3.12)

According to the inequalities (6.3.4), (6.3.5), (6.3.8), (6.1.15), (6.1.16), (6.1.18), and (6.1.19), only the sign of C is unambiguous: C > 0. Three cases may therefore be distinguished:

(I) dq < O, (II) dq = 0,

(III) dq > 0.

Case I . This case corresponds to the steady-state solution $2 in Figures 5.3 and 5.4 where A and B are positive. The sign of D is indeterminate. The characteristics of the adjustment process are determined by the characteristic roots ~ of tile characteristic equation

IA; -

Hence

,~1,2 :

,~ B I = 2 8 - - (D + A))o - - (BC - - AD) . (6.3.13) D - - 2 J

D + A ~ ~/iD + A) ~ -}- 4 (BC - - A D )

2 (6.3.14)

It follows from the above equation that a necessary condition for steady growth (corresponding to $2 in Figures 5.3 and 5.4) to be stable is that D < 0. On the other hand, B C - - A D is positive for D < 0. Hence, the adjustment process is then nonoscillatory and the characteristic roots have opposite signs - point $2 in Figures 5.3 and 5.2 is a saddle point. Steady growth at S~ is unstable. The relevant phase diagram is presented in Figure 6.3.1.

Except for the cases where the economy is moving by chance along the arrows T1S or T2S, the steady-growth state will not be reached if growth is non-steady. So the conclusions of the short- run analysis concerning the stability of $2 also hold in the intermediate run.

Case I I . In this case the steady-state wage curve touches the full employment line H1H~ at qt = 4. In equations (6.3.11) and (6.3.12), A = 0 arid B is positive definite. The characteristic equa-


i t = 0

w T2~

• =

Figure 6.3.1

e t

w t

$ W

~ t = 0

/ ~ = 0

, 3

Figure 6.3.2

y

e t

606 s.K. KUIPERS

tion is

Hence,

--Z B I = 2 2 - - DZ - - BC. (6.3.15)

D -- 2 I

2) ± + 4BC ~,1, 2 --- ( 6 . 3 . 1 6 )

2

Since B > 0 and C > 0, B C > 0. The adjustment process is there~ fore nonoscillatory, and for D < 0 the characteristic roots are again of opposite sign. In this case equations (6.3.11) and (6.3.12) once more define a saddle point. For either D > 0 or D < 0, steady growth is unstable.

Case I I I . This case corresponds to point Sa in Figures 5.3 and 5.4. Now A is negative definite. The sign of B is indeterminate. It follows from equation (6.3.14) that D < 0 and B < 0 are sufficient conditions for the adjustment process to be damped. It is cyclically damped if the discriminant (D + A) 2 + 4(BC - - A D ) < 0

and nonoscillatory damped if this discriminant is positive definite. So it may be concluded that $3 in Figures 5.3 and 5.4 depicts a stable point of steady growth with full employment prevailing. The phase diagram 6.3.2 shows a nonoscillatory damped adjustment process.

7 CONCLUDING REMARKS

In the preceding sections a demand and supply model of economic growth has been developed. By means of this model a number of characteristics of the growth process have been investigated. Special attention has been given to the causes and consequences of growth disequibria and to the determinants of income distribution.

The analysis leads to the conclusions that three growth situations must be distinguished:

(1) output is restricted by effective demand, (2) output is restricted by effective supply, (3) output is restricted by the size of the labour force. In the first case output is adjusted to effective demand. The

market of produced goods is in equilibrium, but the labour market is not necessarily in equilibrium. Here steady-state growth of output may be accompanied by a constant rate of unemployment of

A D E M A N D A N D S U P P L Y M O D E L OF E C O N O M I C G R O W T H 607

the labour force. Furthermore, the price level is not necessarily constant. During a process of s teady state growth, the price level may rise or fall at a constant percentage. Distributive shares are determined by demand as well as by supply factors.

In the second case the profit margin is so low as to make entrepreneurs unwilling to satisfy effective demand: output is determined by effective supply. The market of produced goods is in excess demand and the labour market is in excess supply. In a situation of s teady growth, the rate of unemployment and the degree of excess demand of produced goods are constant. Unem- ployment as well as income distribution are primarily (but not entirely) determined by supply factors. The rate of inflation is not necessarily zero.

In the final case output is determined by the size of the labour force. The market of produced goods is in excess demand. As in the second case income distribution is primarily (but not exclusively) determined by supply factors. The price level is not necessarily constant.

All this leads to the conclusion that equilibrium growth is not established automatically. Deliberate policy measures are necessary to deal with the disequilibria. It is therefore important to diagnose the cause of the disequilibria correctly. For instance, the cause of unemployment in the first case is entirely different from that in the second. In the first case it is partly due to a shortage of effective demand. Hence, unemployment may be fought by a demand-oriented policy; that is, fiscal or monetary policies. In the second case unemployment is mainly caused by a profit margin which is too low. So unemployment may be fought most effectively by a supply-oriented policy; namely, wage and price policy.

Regarding the present situation in the Netherlands, there is some reason to believe that unemployment is due not so much to a shortage of effective demand as to a profit margin which is too low. 50 Because of the strong rise in the labour share of the national income, the Dutch economy might have arrived at the supply- restricted part of the output curve. If this is true, then a further fall in the profit margin is much more dangerous for employment

a0 See, e.g., Cent ra l P l a n n i n g Bureau , Centraal economisch plan, The Hague , 1972, p. 18, pp. 77 79 and pp. 179-181. For a su rvey of the large fall in the ra t es of r e tu rn of D u t c h indus t r i e s in the ' s ixt ies , see also: Centra l P l a n n i n g Bureau , De Nederlandse economic in J:973, P a r t I, The Hague , 1970.

608 s.K. KUIPERS

by inducing a slower growth in effective supply than by entailing a slower growth in effective demand. 51

Another important conclusion which follows from the analysis given above is that income distribution is determined by an inter- action between demand and supply factors. Although in some situations supply factors prevail (the 'second' and the 'third' case), the distributive shares are never solely determined by these factors. I t must therefore be concluded that neo-keynesian as well as neo- classical theories of income distribution are one-sided.

Finally, it must be acknowledged that in one respect the analysis given above is not entirely satisfactory. This is because monetary influences have been almost entirely neglected. The liquidity quota is considered to be constant and determined autonomously by the central bank. Moreover, in situations of excess demand of produced goods, it is assumed that entrepreneurs have easy enough access to the money market to force consumers to save enough so that pro- ducers can carry out their investment plans. The first assumption is no doubt unrealistic. If it is dropped, it is necessary to complement the model of the real sector with a model of the banking sector. Through such an extended model, it should be possible to solve the problem of the extent to which real and monetary growth influence each other. Simultaneously, the question of the extent to which entrepreneurs can force consumers to save might be investigated.

SU?/lC~ta~'y

A DEMAND AND SUPPLY MODEL OF ECONOMIC GROWTH

A demand and supply model of economic growth has been developed. By means of this model a number of characteristics of the growth process have been investigated. Special attention has been given to the causes and consequences of growth disequilibria and the determinants of income distribution.

The analysis leads to the conclusion that three growth situations must be distinguished: output is restricted by effective demand, by effective supply, and by the size of the labour force. The causes of growth disequilibria and the determinants of income distribution differ in each of these three cases. In this respect the model is more general than tra- ditional post-keynesian, neo-keynesian and neo-classical growth models.

5J A similar view, formulated somewhat differently however, will be found in President Zijlstra's 'General Survey' in: De Nederlandsehe Bank, N.V., Report [or the Year s97 r, Amsterdam, 1972, p. 13.

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A demand and supply model of economic growth