7. T. W. Swan: “The Principle Of Effective Demand—A ‘Real Life’ Model”

Several writers have pointed out that “model sequences” without a realistic statistical basis, and lacking the analytical flexibility of general equilibrium theory, are likely to lead to results the relationship of which either with reality or with particular theoretical assumptions can be ascertained only by a laborious process of trial and error. On the other hand, Professor Tinbergen’s great statistical synthesis of the US economy (Statistical Testing of Business Cycle Theories, Part II) is a nebula rather than a solar system, the theoretical laws of its motion being too complicated to be grasped as a whole; while general equilibrium, of the kind established by the (explicit) system of the General Theory, or by Professor Pigou in his Employment and Equilibrium, is in the real world “something of a Cheshire cat”. The clue to a satisfactory integration of general equilibrium theory with “dynamic” sequence analysis has already been given by writers such as Professor Lange (Economica, February 1938), Dr Kalecki (Essays in the Theory of Economic Fluctuations, 1939) and Mr Kaldor (Economic Journal, March 1940), working on the foundations of the General Theory. Moreover, the diagrammatic presentations of these writers, taken in conjunction with Mr Colin Clark's pioneering statistical studies of the “Multiplier” and Professor Tinbergen’s work, readily suggest how a simple but “dynamic” general theoretical system might be used as the framework of a statistical model of an actual economy.

The principle followed has been to choose the simplest assumption which is a priori not unreasonable and a posteriori not inconsistent with the statistics. But it must be recognized from the beginning that the use of aggregates covering a diverse economy, the breaking up of the flow of time into arbitrary “periods”, the use of uncertain statistical series, and other unavoidable features of the statistical model, impose severe and inherent limitations on the realism of the model.

P. 25.

For reasons of statistical convenience, all variables in the model are in practice measured on an annual basis, but at quarterly intervals.

General Theory, p. 51.

This time-lag corresponds with what Lord Keynes, not altogether felicitously, has called “the period of production” (General Theory, p. 287).

It is interesting to note that the Keynesian definitions of aggregate supply and aggregate demand price in terms of expectations (General Theory, pp. 24 and 25) implicitly require a dynamic theory in which the magnitudes dated; without this, it is impossible to distinguish the Aggregate Supply Function from the Aggregate Demand Function. Professor D.H. Robertson seems to have been misled by the ambiguity of the General Theory in the dating of the two sets of expectations of proceeds (Essays in Monetary Theory, p. 114). “Suppose”, he says, “that entrepreneurs … expand output in the belief that \({\Delta }Y\) will equal \({\Delta }Z\). Their disappointment must surely not be represented … as due to a divergence between aggregate demand price and aggregate supply price; for in the case supposed these two are equal”. On the above interpretation, Professor Robertson is here looking only at the Aggregate Supply Function, and has left the Aggregate Demand Function right out of the picture. As a result, he goes on to accuse Lord Keynes, in effect, of neglecting precisely the distinction which it is the whole purpose of the Keynesian Functions to bring out—i.e. the distinction between (i) the state of expectation which led up to the current level of employment (and the maintenance of which would justify the maintenance of that level of employment), and (ii) the revised state of expectation which confronts employment at its current level (and which will in tum lead up to a new level of employment in the next period). It is, of course, possible to interpret the functions in a “static” sense; but not in terms of expectations (see below).

Appendix, paragraph (1).

For simplicity, no allowance has been made for secular trends, although possibly better results might have been obtained had this been done. It would certainly have been necessary if the period covered had been much more than eleven years.

General Theory, p. 24.

There is a difficulty here, which is partly the result of trying to represent the actions of individual entrepreneurs in terms of relationships between aggregates (and to this extent is present in the General Theory), and partly the result of breaking up the flow of time into arbitrary units (and to this extent is peculiar to the method of sequence analysis). For if we imagine each entrepreneur as forming a definite expectation of future proceeds independent of his own price and output, then the demand curve confronting each entrepreneur is, of course, of unit elasticity, and marginal revenue zero, with absurd consequences for price and output policy. Hence the term “expectation of proceeds” in Lord Keynes's definition cannot be taken without qualification as it stands. In one sense, the elasticity of demand (on our assumptions) is in fact unity—but only in the sense of demand in the aggregate. This is not the picture seen by the individual entrepreneur. We must imagine that the individual entrepreneur receiving (for instance) an increased stream of sale-proceeds, takes this to mean a shift of his demand curve to the right, and tentatively expands his employment and output at the price set by his new demand curve. Thus each individual entrepreneur's expectation of proceeds is conditioned by his own current view of the position of his demand curve and by his price-output policy, aimed at equalizing marginal revenue (as it appears to him) and marginal cost. But unless the individual expectations of all entrepreneurs add up to the aggregate proceeds which are determined by the system as a whole, there will be an outstanding balance either of expectations exceeded by the results, or else of expectations disappointed by the results, and a corresponding further adjustment of entrepreneurs’ views about price-output policy. The upshot of this process, looked at from the point of view of averages and aggregates, is implied in Lord Keynes's definition of “aggregate supply price” quoted above. Paradoxically, in sequence of analysis we take account of the fact that the process of adjustment goes on over time, and that each employment adjustment lags behind the state of income and expectation which stimulated it, only by assuming that the entire adjustment takes place in the (infinitesimal) interval which occurs after the curtain falls on the tableau of one “period” and before it rises on the next. (For an example of puzzlement on the point dealt with above, Cf. F.H. Knight, Canadian Journal of Economics and Political Science, February 1937, p. 103.)

For convenience of reference, the meaning of the symbols is here recapitulated.

The dependent variables, whose movement is determined in the working of the model, are employment, N; real output, X; unit supply price, P; marginal cost, Q; consumption, C; income, Y; private investment, I; imports, U; aggregate supply price, Z; aggregate demand price, D; The independent variables are the sum of exports and public investment, E; and the influence of import­price, the landed price-level of imports, V.

All variables (except N and X) are measured in wage­units, but the absolute magnitudes of the figures to be inserted in the equations must be ascertained from the description of the statistical series at the end of the Appendix. Counting Y and \(Y_{t - 1}\) as separate variables, there are eleven dependent variables and only ten equations to determine them. In order to make the system determinate from the point of view of sequence analysis, it is necessary to take Y_t and \(Y_{t - 1}\) as given at the beginning of the sequence; thereafter, the Y_t of one period is, of course, the Y_t and \(Y_{t - 1}\) of the next. A knowledge of the actual wage-unit at any time enables the money value of any variable to be computed. Thus we might add another equation, writing W, for the wage-unit (regarded as an independent variable) and £Y, for the money value of income (and similarly for other variables):

When “full employment” is reached, N becomes a known constant and its place as a dependent variable is taken by W_t.

If saving is defined as “saving out of disposable income” a la Robertson \(\left( {S_{t} = Y_{t - 1} - C_{t} } \right),\) then an excess of aggregate demand price over aggregate supply price is identically an excess of investment plus exports over saving plus imports, or, in a closed economy, an excess of investment over saving. On this definition, C, being a function of \(Y_{t - 1}\), S_t is also a function of \(Y_{t - 1} .\) The same result is achieved if saving is defined as “saving out of ex ante income” (ex ante saving), provided that it is further assumed that ex ante income for the next period is equal to the realized income of this period. On this definition, saving is a function neither of Y, nor \(Y_{t - 1}\), but may be regarded as the sum of \(\left( {Y_{t - 1} - C_{t} } \right)\) and \(\left( {Y_{t} - Y_{t - 1} } \right)\) the first expression being a function of income, and the second expression zero unless income is changing.

Thus it is perhaps legitimate to say that “income must change in order to ensure the equality of S and I” (Cf. the contrary view taken by Professor Haberler, Prosperity and Depression, third edition, 1941, p. 193 n.). It is an advantage of the General Theory approach, used in the model, that it avoids these complications by concentrating attention on consumption, the determination of which (as Lord Keynes says, p. 65) “truly lies within the power of the individual”, and which may be expressed straight­forwardly as a function of income. In the model, no distinction is made between ex post and ex ante investment, for reasons given in the Appendix, paragraph (9), footnote.

The years 1928–1939 have been chosen for the model sequence because certain of the statistics are not available for years before 1928–1929, and because the development of war economy after June 1939 upset the “basic functional relationships” of the system (and incidentally arrested the incipient depression which is apparent in the movement of “equilibrium income” in Fig. 7.3.

In the case of unit supply price, the comparison is, of course, with an index of the “realized” price-level, which (for reasons explained in a footnote to paragraph 9 of the Appendix) may be expected to be greater or less than unit supply price according to whether income is rising or falling. In fact, the divergence between the actual index and the calculated unit supply price is in the right direction in eight years out of the eleven. The significance of the series at the top of the diagram, showing income and equilibrium income in wage-units, is explained below.

General Theory, p. 78.

In Professor Pigou’s terminology (Employment & Equilibrium, p. 33) the position is one of “short-period flow equilibrium”. The discrepancy between aggregate supply price and aggregate demand price in all other positions is identical (in a closed economy) with Professor Samuelson’s “virtual inequality of saving and investment” (American Economic Review, September 1941, p. 546).

The determination of income is thus independent of the shape and position of the Aggregate Supply Function, whereas employment depends on both Aggregate Functions (Cf. the method of constructing the Aggregate Demand Function). It follows that we may suppose the Aggregate Demand Function to shift while the Aggregate Supply Function remains unchanged, but if the Aggregate Supply Function shifts the other Aggregate Function must also shift, and it must shift in such a way that the two curves cut an unchanged level of income but a different level of employment. Hence in the model the result, for instance, of a rise in the degree of monopoly (which means an upward shift in the Aggregate Supply Function) is to reduce employment while leaving income unchanged. Whether technological advance increases or reduces employment depends on whether it reduces the unit supply price sufficiently to offset the effect on aggregate supply price of higher output at any given level of employment. This analysis leaves little substance in W. Leontieff’s charge against Lord Keynes of “open logical inconsistency” in connection with the interrelations between the two functions (Quarterly Journal of Economics, February 1937, p. 350).

If the model were a closed economy without public investment, or in which the government fixed public investment in terms of wage-units, changes in money wages would merely change prices and have no effect on the level of income (measured in wage-units) or on employment. Similarly, in the system of the General Theory, where the rate of interest is included as a determinant of investment, changes ID money-wages affect employment only through the rate of interest because the quantity of money is the only variable in the system not fixed in terms of wage-units. Thus the Keynesian view that unemployment 1s consistent with equilibrium does not involve, as Professor Knight claims, “the essential assumption of the (downwardly) fixed supply price for labour” (Canadian Journal of Economics and Political Science, February 1937, p. 104). Whether it is realistic to assume that the “basic functional relationships” of the economy are stable in terms of wage-units is another matter. For example, Professor Pigou obtains his conclusion that unemployment is not consistent with equilibrium, unless money wages are rigid, by assuming (in Keynesian terminology) that the propensity to consume shifts with changes in money wages, the consumer's desire to accumulate further assets diminishing when a fall in money wages increases the real value of his existing stock of money (Economic Journal, December 1943, p. 349).

This is the sum (“marginal propensity to consume” plus “marginal propensity to invest” minus “marginal propensity to import”), and is the gradient of the family of curves relating aggregate demand price to income at the top of Fig. 7.2.

The gradient of the Equilibrium Income Function (from Eqs. (4), (5), (6) and (8)), for levels of income above 538 at which private investment begins to rise above its bedrock level. is:The maths in this footnote need to be reset. where the expression in brackets is the “marginal propensity to spend at home”. Writing \(\frac{{{\text{d}}S}}{{{\text{d}}r}}\) for the “marginal propensity to save” \(\left( { = 1 - \frac{dC}{{dY}}} \right)\) the stability condition—viz. that the gradient must be positive—becomes \(\frac{{{\text{d}}I}}{{{\text{d}}Y}} < \frac{{{\text{d}}S}}{{{\text{d}}Y}} + \frac{{{\text{d}}U}}{{{\text{d}}Y}}\), which for a closed economy is the familiar condition that the income-investment curve should cut the income-saving curve from above (Cf. N. Kaldor, Economic Journal, March 1940, pp. 79–80).

The above expression for the gradient of the Equilibrium Income Function will also be recognized as the familiar formula for the “multiplier”, in a compound version (allowing for the dependence on income of private investment and imports, as well as of consumption, and representing “autonomous changes in imports” in the “multiplicand” by changes in V). An example of the “multiplier” technique under the conditions of the model seems to cast serious doubts on the usefulness of this concept. In the illustration of Fig. 7.1, the model’s operation given and depicted in E + V was assumed to fall after period (3), in which income was 785, by 20. With income at 785, the value of the multiplier given by the above formula is 3.5. The “multiplier” technique would therefore predict a fall in income of 70. But the “multiplier” formula assumes that at the time of the fall in the Determinants income is in equilibrium; in fact, it was below equilibrium, and below even the lower equilibrium position resulting from the fall in the Determinants-income would thus not fall, but continue to rise. Even if income had been in equilibrium at 785, the income fall (in equilibrium) resulting from the fall of 20 in the Determinants would have been, not 70, but 90, the discrepancy arising from curvilinearity.

Similar examples might have been taken from the actual course of events 1928–1939. In any case, the fact that the value of the “multiplier”, as calculated from the formula, varies so widely, e.g. from 16 when income is 600 to 2.4 when income is 900, suggests a severe restriction on its practical usefulness.

The reader who is interested will find that many of the questions raised by Professor Haberler regarding the limitations of the “multiplier” technique and the relationships between the various “multiplier” concepts (op. cit., pp. 455–473) can be given concrete answers from the model's equations. It is also possible to evaluate for the model most of the great variety of “multipliers”—“simple” and “compound”, “ordinary” and “truncated”, “horizontal” and “cumulated”—distinguished in articles by Professors Lange and Samuelson in Econometrica, July–October 1943.

The reason for this can be visualized by imagining the method of construction of the Aggregate Demand Function (see above) to be one of “bending” the family of curves in Fig. 7.2 which relate aggregate demand price to income and the gradient of which is the “marginal propensity to spend at home”—around the curvature of the Aggregate Supply Function.

See footnote 22.

It is interesting to speculate as to whether this corollary may contribute to the explanation of the well­known empirical phenomenon of a sharp recession and more gradual recovery.

This proposition is, of course, subject to the proviso that there will be no tendency to approach equilibrium at all if the “marginal propensity to spend at home”, exceeds unity at the “equilibrium” point (the Aggregate Demand Function cutting the Aggregate Supply Function from below).

The anti-depression policy described here is, of course, now recognized as one of “beggar my neighbour”; but in the 30s it was “sauve qui peut”, and even the Treatise on Money still to come. (It is unlikely, in view of the small proportion of Australian imports in world trade, that greater Australian imports would have meant any significant improvement in Australian exports.)

Let £stg.U be the actual average money value of imports per annum in terms of sterling, and £stg.V the actual average money value of V in terms of sterling. Equation (6) of the model givesand the condition that sterling out-payments must not be increased gives

Hence the level of V consistent with this condition is

If Y = 730 (as postulated), and if \({\pounds}{\text{stg}}.V = 87\) and \({\pounds}{\text{stg}}.U = 71\) (the actual values 1929–1930 to 1934–1935 in appropriate units), then v = 133, or 152% of £stg.V.

This degree of depreciation actually occurred at the beginning of 1931, but at the end of that year the depreciation was reduced to 25%.

The writer’s personal view, in the Australian circumstances of 1929, would be in favour of a moderate rise in exchange rates (largely with the social objective of preventing too great a fall in rural incomes) and a substantial programme of public investment—including expenditure on social services and housing as well as developmental works—leaving external equilibrium to be maintained by exchange control and import quotas, but maintaining internal equilibrium at or above the 1928–1929 level of income and employment.

There emerge two conclusions which are not without significance for the international negotiations regarding monetary, commercial and employment agreements:

In “multiplier” terminology, each “reaction” in the Kalecki–Kaldor models represents the completion of the full “multiplicatory” process, with the dependence of private investment on the level of income or employment recognized by making an appropriate adjustment in the “multiplicand” at the end of each such process; whereas in the present model each “reaction” is only a single “round” of the “multiplicatory” process, and the dependence of private investment on income is recognized in the “multiplier”, not the “multiplicand”. However, it is true that after a relatively few “rounds” of the “multiplicatory” process the bulk of the adjustment will have been completed. Hence, on a less strict view, the time required for a single “reaction” in the Kalecki–Kaldor models could be brought within finite limits by assuming that for practical purposes the adjustment may be regarded as complete when a substantial proportion—say 90%—of the change in income has been achieved. In this case, the “reaction” time, although finite, would not be uniform unless the “marginal propensity to consume” were uniform at all levels of income. Dr Kalecki (op. cit., p. 136) in fact makes this assumption.

Here Professor Robertson might perhaps quote the Unicorn's advice about managing looking-glass cake: “Hand it round first and cut it afterwards”. However, in fairness to both authors, it should be pointed out that the concept of a “shuttling” process between the curves is not essential to the Kalecki–Kaldor models: it is not necessary to go beyond the proposition that income increases so long as “investment” exceeds “saving”, and vice-versa. But in this case the advantage of “sequence” analysis is lost, since there is no explicit means of recording the passage of time. In fact, Mr Kaldor does not make use of the “shuttling” concept, and Dr Kalecki’s use of it (op.cit., Fig. 14, p. 142) is possibly justified on the grounds mentioned in the preceding footnote.

R.F. Harrod, The Trade Cycle, and An Essay in Dynamic Theory, Economic Journal, March 1939. With the help of the Aggregate Supply and Aggregate Demand Functions, this analysis might perhaps be made more flexible, since it need not be so closely tied to the concept of a “constant rate of advance”.

In the interest of stable functional relationships, it would perhaps be better to measure different variables in terms of the different units appropriate to each relationship (e.g. cost-of-living, price-level of investment goods, etc.). However, a multiplicity of units would greatly complicate the system, and in fact the wage-unit seems to be a very satisfactory compromise. (For the implications of this choice, see footnote 21.)

Mr Colin Clark, in correspondence with the writer, has taken a different view of the three functional relationships dealt with in this section, and has rightly criticized the realism of some aspects of the forms here assumed. Mr Clark's criticism is based partly on different statistical estimates, and partly on considerations relating to the likely magnitude and movement of marginal user cost and the degree of monopoly. Although Mr Clark has been good enough to suggest alternative forms which would overcome his objections, pressure of duties unfortunately precludes any revision at this stage. In any case, a truly “realistic” approach to the Aggregate Supply Function is an economy such as the Australian would undoubtedly involve the inclusion of a definite distinction between the rural and non-rural sectors.

Some references are M. Kalecki, Essays in the Theory of Economic Fluctuation, p. 35; A.C. Pigou, Employment and Equilibrium, pp. 47–49; R.F. Harrod, The Trade Cycle, p. 21; Allen and Bowley, Family Expenditure, p. 125; D.H. Robertson, Canadian Journal of Economics and Political Science, February 1939, p. 124.

The absolute smallness of the proportion is not directly relevant, owing to the element of arbitrariness in the absolute magnitudes of the figures to be inserted (Cf. paragraph (1) above). However, this is one of the points against which Mr Colin Clark has directed valid criticism.

This inverse function is what Lord Keynes (General Theory, p. 280) calls the “employment function”.

P. 96.

Quarterly Journal of Economics, November 1939. Cf. also A.H. Hansen, Fiscal Policy and Business Cycles, pp. 268–270.

Some references are to A.H. Hansen, Fiscal Policy and Business Cycles, pp. 330–331; J.R. Hicks, Value and Capital, pp. 225–226; H.D. Henderson, J.E. Meade, P.W.S. Andrews, A.J. Brown, R.S. Sayers and others (various articles in connection with the two Oxford Research Group questionnaire enquiries, Oxford Economic Papers Nos. 1, 2 and 3); J. Tinbergen, Statistical Testing of Business Cycle Theories; M. Kalecki, Essays in the Theory of Economic Fluctuations; M. Ezekiel, American Economic Review, June 1942; E.A. Radice, Econometrica, January 1939. It should be noted that the assumption that the influence of changes in the rate of interest on investment can be neglected is specifically based on the empirical evidence of stability in the relevant interest rates; this is still consistent with the view that a change to very low or very high rates would have an important influence. (On this point, Cf. Keynes's comment, quoted Ezekiel, op. cit., p. 283.)

O. Lange, Economica, February 1938; J.R. Hicks, Econometrica, April 1937; M. Kalecki, Essays in the Theory of Economic Fluctuations; N. Kaldor, Economic Journal, March 1940.

Cf. Mrs Joan Robinson, Economic Journal, 1942, p. 353. See also text, Section V, where the influence of the growth of productive capacity is introduced.

Dr Kalecki (op.cit, p. 126) suggests 3–6 months for this lag.

No distinction is made between realized (ex post) and planned (ex ante) investment, i.e. it is assumed that there are no unforeseen changes in stocks. Taken in conjunction with the assumptions made regarding expectations, this implies a further assumption, viz., that changes in demand are automatically prevented from affecting stocks by the appropriate price adjustments (e.g. “auction” price-fixation). Hence the “realized” price in the model is not equal to the unit supply price, P, but greater or less according to whether income is rising or falling, the ratio of “realized” price to supply price being in the same proportion as current income to the income of the previous period. Discrepancy between ex post and ex ante investment has been excluded from the model on the ground that unforeseen stock changes lead to complicated entrepreneurial behaviour of a kind difficult to reconcile with a simple model (Cf. L.A. Metzler, Review of Economic Studies, August 1941), especially since this behaviour is concerned with adjustments of the type dealt with in footnote for which the appropriate “period” is much less than the three-month unit “period” of the model. The general principle of exclusion is that there is no place for day-to-day experiments in price-output policy in a model with this unit period.

It would be more satisfactory to use here some sort of index of the ratio of the import price-level to the price­level of “domestic” goods competing with imports, but no adequate index of the latter price-level is available. On the other hand, if the level of money wages were taken to represent approximately this “domestic” price-level (as suggested by Taussig and Viner, see R. Wilson, Capital Imports and the Terms of Trade, p. 94), then the use of the import price-level (which is, of course, to be measured in wage-units), as proposed in the text above, might be regarded as equivalent to the use of the ratio of import to “domestic” prices.

In a few instances it has been necessary to bring up-to-date the statistics obtained from sources acknowledged below by adding estimates for 1938–1939. This has been done on a comparable basis, generally by making use of unpublished official or semi-official estimates.