THE GEOMETRY OF MACRODYNAMIC BALANCE:

A NOTE*

DAVID R. RICHARDSON

Legislative Research Service Parliamentary Library

Parliament House Canberra

In a recent article in this journal Eichner [ l , see also 21 offers an alternative to the Hicksian IS and LM curve analysis which, he claims, provides “a far more useful device for organizing and presenting a macrodynamic analysis” [ 1, p. 541 . The purpose of this note is to rework Eichner’s analysis so as to elaborate on some points given insufficient attention by Eichner. In so doing it becomes apparent that the model may in fact be “richer” than Eichner’s original.

In a simple economy enjoying equilibrium steady-state growth, demand for final out- put is growing just sufficiently to warrant the investment expenditures being undertaken [ 1, p. 551 . Entrepreneurs’ expectations are not being disappointed within a dynamic equilibrium. Note, and this is crucial, that steady-state growth is characterized by two conditions. First, the “demand conditions”; planned sales equals planned purchases in any one period and will be growing at the same rate over time. Secondly, the “capacity condition”; the growth in the capital stock, making appropriate adjustments for technical progress, is growing at the same rate as the growth in planned sales. The original Harrod- Domar models set out to examine the behaviour of any economy in which both conditions are met. As will be shown below, Eichner pays insufficient attention to the capacity conditions in his extensions of the basic model.

If we utilize a Kaldorian technical progress function,’ as does Eichner himself, then our capacity condition for steady-state growth requires that the economy must lie on some function E in Figure 1, where G is the rate of growth of aggregate output, and S and I the respective rates of growth of savings and investment. Without technical progress the E function is merely the 45 degree line emanating from the origin.

Eichner then introduces two behavioural relationships in which the rate of growth of both savings and investment are functions of the actual or short-run rate of growth of

*This note was written while the author was employed by the University of Western Australia. The author wishes to acknowledge the assistance of Dr. A. Petridis and Professor A.S. Eichner. In this formulation technical progress is embodied only in new capital equipment.

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FIGURE 1

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G

output.2 These relationships are reproduced in Figure 2. Assuming steady-state growth, or Eichner’s secular g r ~ w t h , ~ equal to G,, the S and I schedules must each also intersect Eat Gs.

* *

FIGURE 2

S

I I

I / I

* * G Gs

*These are described in [ 1, p. 56, et. seq.] . 3Eichner distinguishes between warranted and secular growth rates, the latter being subject to cyclical influences. However, this distinction need not concern us here and the terms will be used interchangeably.

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FIGURE 3

(a) Oligopolistic Sector

I X G

s,r I (b) Government Sector

(c) Economy as a Whole sJ I

DECEMBER

* G

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In his economy-wide model Eichner treats government outlays as investment and receipts as savings. This is of course quite valid in usual textbook treatments where the problem is the determination of a static equilibrium level of income. However, govern- ment outlays clearly cannot be treated as investment in the functional sense of that term since government outlays do not necessarily add to the existing stock of productive capi- tal goods. In addition, it should be noticed that Eichner’s broader definition of firms’ investment also includes expenditures, such as advertising, which likewise do not augment the capital stock [2] Nevertheless, Eichner suggests that the government, by acting so as to produce an upward shift in its own I schedule, ZG to in Figure 3(b), will cause the secular growth rate to increase from G, to G, in Figure 3(c). As the aggregate growth in “injections” equals the aggregate growth in savings, the demand conditions for steady- state growth will continue to be satisfied. However, there is no guarantee that the capacity condition will be satisfied at G, . Indeed, as we attempt to show, this condition will not normally be satisfied. But rather than causing us to dismiss Eichner’s analysis we shall extend it explicitly to consider the problem of capacity growth.

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*

To simplify the following analysis we assume only two sectors, Eichner’s oligopolistic sector and the government sector. Furthermore, we shall assume all government “invest- ment” is expenditure on the output of the oligopolistic sector. This assumption is not too unrealistic if we consider government employees as simply intermediaries in the process of spending government funds. The implication is of course that only investment under- taken in the oligopolistic sector can be considered as augmenting the capital stock. We shall also ignore “non-productive” components of oligopoly sector investment.* It is important from here on, though Eichner fails to incorporate this consideration, that any equilibrium steady-state growth must lie on the E function of Figure 1. This function is superimposed in Figures 4(a) and 4(c) in which we assume an economy initially growing at a steady-state rate of growth G,. In our analysis we consider only the case where Zo intersects E from above. This is keeping within the spirit of Eichner’s analysis since E gives the rate of growth of investment necessary for capacity to expand at the same rate as planned purchases. But to the right (left) of G , the long-run rate of growth in the latter is less (greater) than the short-run rate of growth of output. I . is assumed to respond only partially to changes in the short-run rate of growth. We now examine the consequences of the attempt by the government to increase the growth rate to G, using the type of policy advocated by Eichner.

*

*

*

* From Figure 4(c) it is clear that the growth rate G, satisfied only the demand condi-

tion for steady-state growth. By our second assumption, that all purchases are made on the output of the oligopolistic sector, and only investment in the oligopolistic sector is productive, then the equilibrium growth rate according to our capacity condition can

41t may well be that for many purposes it is valid to think of past advertising as having created a stock of “good-will” for or some “predisposition to buy” from a particular company. However, this in no way helps in the ability to provide for fmal demands.

’Such “non-productive” elements of Eichner’s definition of investment could be catered for by a further subdivision of investment. But this would not affect the following argument.

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* I

O 2

* * I . = so

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FIGURE 4

(a) Oligopolistic Sector

PE

DECEMBER

I I * * * G

GS GI (b) Government Sector

I I * * * G GS GI

(c) Economy as a Whole / S

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* # * # only increase by ZO - Zo, or G2 - G, in Figures 4(a) and 4(c) respectively. The conse- quences of this should be apparent. The demand for the output is growing more quickly than the capacity to produce that output. Eventually the consequences must be infla- tionary. If instead G, was to be maintained then, from Figure 4(9, the rate of growth of investment in the oligopolistic sector would need to increase to I , . As we have drawn the I function this will not eventuate.

Of course if GI were to be regarded as the new long-run rate of growth of output then firms would in fact wish to raise the rate of growth of investment to precisely I , in order to cater for that rate of growth of planned purchases. This raises an extremely important issue. The whole point of Eichner's discussion of the megacorp [2] and espe- cially its investment and corporate-levy, ie. pricing decisions, is that the Z, and S

#O schedules are likely to intersect on E a t the expected secular growth rate. Hence, were GI to become the expected secular rate of growth of sales then megacorp would change its behaviour such that I ' , and S', are now the relevant functions. Notice also that ever- increasing government deficits would now no longer be necessary for steady-state growth.

This raises the following dilemma for government policy directed toward raising the growth rate. For the government to be successful in raising the secular growth rate to GI it must convince the oligopolistic sector that this rate is indeed the equilibrium growth rate. This will re uire overnment policy to produce a growth rate in aggregate demand of G in excess of G, until the expected secular growth rate does indeed increase from G, to #1 G I . Only then will the behaviour of the oligopolistic sector adjust to provide the growth in capacity to warrant a growth rate of G I . If in the interim full capacity is reached then (demand-pull) inflation may well result. Inflation, by interfering with the informational content of the price system, may actually worsen the situation if it causes the Zo function to shift bodily downwards.6 It is possible that such a process may have characterized the Australian economy during the early 1970s though a discussion of this matter is beyond the scope of this note.' The crucial thing to note however is that the effect of policy depends critically on the responsiveness of megacorps' expectations relative to the time taken before the policy measures push against full capacity. Worse still, neither of these factors can be expected to remain constant over time.

An important implication of this type of analysis is the influence of an economy's history in determining behaviour, and the effectiveness of policy at any point in time. In Figure 5 we compare two llke countries A and B in which the historical norm had been growth rates of GA and GB respectively but which are both now growing at GA. Attempts by their governments, through the types of policies outlined by Eichner, to

1

#

2

#

#

2

*

* B g *

*

* * *

6This possibility, in a different context, was suggested by, among others, M. Friedman [3] . There are likely to be further difficulties involved in the transition from Gs to G I . However these take us beyond the scope of the present note.

'Eichner in private correspondence indicates his belief that excess capacity in the oligopolistic industries will permit non-inflationary responses to temporary increases in demand. His own view is that inflation is due to factors on the supply side [ 21.

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increase the growth rate to GB are likely to be relatively easy in country B but beset by all the difficulties just described in country A . Hence, the necessity stressed by post- Keynesians of setting analysis firmly within the context of the history of the economy in which we are interested.

FIGURE 5

I

I I I I 1 I # * # G* GB G

REFERENCES

1. A.!;Eichner, “The Geometry of Macrodynamic Balance”, Australian Economic Papers, vol. 16, 1 Y I I .

2. A.S. Eichner, The Megacorp and Oligopoly, Micro Foundations of Macro Dynamics (Cambridge: Cambridge University Press, 1976).

3. M. Friedman, “Nobel Lecture: Inflation and Unemployment”, Journal of Political Economy, vol. 8 5 , 1977.