NOTES

ECONOMIC GROWTH L I D CAPITAL A C C ~ l U L A T I O N A Comment

The propositions in Professor Swan’s article1 agree pretty well with my Accumzilation of Capital, and I cannot quite understand what it is in the book that he finds so indigestible.

I am pleading for the observance of two simple methodological rules for the conduct of theoretical analysis, which are never disputed in principle though often violated in effect. The first is to draw a clear distinction between a comparison of positions which differ in some specified respect and an analysis of a change taking place in a given position. The second is not to express a quantity without stating the units which it is a quantity of.

Professor Swan violates both rules in the first part of his article , and then tries to excuse himself in the appendix, which seems to be

rather a back-foremost procedure. Let us rather try to restate the substantive propositions without violating t.he rules.

Professor Swan expresses himself in terms of a narrative but his main point lends itself better to terms of a comparison between equilibrium positions (the points 1 and 2 in his diagram).

The main proposition2 is that when there are two economies with the same corpus of technical knowledge and with the same proportion- ate rate of growth in employment, but one with a higher ratio of saving to income than the other, then, when each is growing a t the same rate, in equilibrium conditions, the one with the higher ratio of saving has a correspondingly higher ratio of capital to output.

This proposition is derived by inverting Mr. Harrod’s formula. G is the percentage rate of growth of output per annum, s is the pro- portion of income saved and C is the ratio of the stock of capital to a year’s output. G=s/C or C=s/G. Each economy has a history behind it in which its own G, C and s have been constant for some time a t the values now obtaining. 0 is the same for both of them. I n one economy s is twice that in the other (in Professor Swan’s example). Therefore C is also twice as great.

It is to be observed that in certain conditions it is impossible for C to assume the value required to reconcile a high s with a low G (this is the point that worries Mr. Harrod). I n that case it is s that must give way, or the assumption of full employment cannot be maintained. However, Professor Swan tacitly assumes that the range of variation of C is such aa to give him all the room to manceuvre that he requires.

To make sense of the formula it is obvious that capital and income must be measured in the same units.

Professor Swan wants to measure capital in a physical unit. 1. The Economic Record, Nov. 1956. 2. I am not discussing the treatment of land or of technical progress. Once the

main point has been cleared up they would not present any further difficulties.

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“. . . Capital is made up of a large number of identical meccano sets, which never wear out and can be put together, taken apart, and reassembled with negligible cost or delay in a great variety of models so as to work with various combinations of Labour and Land, to produce various products, and to incorporate the latest technical innovations illustrated in successive issues of the In- struction Book. . . .,’ This is a helpful piece of mental sc&olding, which fuEls the same

purpose as Wicksell’s assumption that different stocks of capital vary only in the length of life of their components. In each case we have a clear meaning to give the concept of a physical stock of capital.

He goes on: “. . . Output consists of goods (including meccano sets) that are all produced and sold at constant price-ratios amongst themselves, no matter how the rates of wages, rents and profits may vary. . . .’, This limits him to a special case. In general, higher wages and a

lower rate of profit entail different relative prices for ditferent goods -in particular different relative prices for capital goods as a whole and consumption goods as a whole. When relative prices are M e r e n t in the two economies, Professor Swan must come off the fence, and say which kind of good he is taking as the mumkraire.

If he means by the rate of saving the rate of output of meccano, then, when the rate of saving is specified, everything is specified in physical terms, but income has to be measured in terms of meccano, 90 that the ratio of income to saving depends upon the price of meccano, and the prospensity to save has to accommodate itself accordingly.

It is more natural (following M i . Harrod) to define income as the value of a year’s output in money of constant purchasing power over consumption goods. This involves only the familiar index-number ambiguity, which can be dealt with by the familiar methods. The ratio of saving to income is then the ratio of the value of a year’s output of meccano to the value of a year’s total output, and a given rate of saving has a larger or smaller content in terms of meccano according as the price of meccano is lower or higher.3 This seems to me to be quite in line with Professor Swan’s areaument, and it was only the excessive caution which made him fiddle the assumptions so as to rule it out that prevented him from stating it himself.

If in reality we could fhd a technical unit of capital correspond- ing to Professor Swan’s meccano or Wicksell’s period of production, then, in comparing two positions with Meren t values of capital per unit of output, we could detect how much of the Merence was due to having a difEerent amount of physical capital and how much to a dif- ferent price per unit of physical capital. We could further detect how much of that difference in price was due to a difference in wages cost

3. It is possible for the price of a piece of meccano to be lower in the economy where the wage rate and the total value of capital are higher, for, as Professor Swan emphasizes, lower interest cost may more.than offset higher wages cost. I do not know why he thinks that I associattd th is with the “pervuse” case in which the degree of mechanization is lower at a hlgher wage rate. Both phenomena, of course. are connected with the element of interest in the cost of capital goods, but otherwise they do not have anything to do with each other.

1957 O W T H AND CAPITAL ACCUMULATION 105

and how much to a difference in the profitmargin, and we could detect how much the difference in the profit margin was due to a difference in capital in the investment sector per unit of output of physical capital and how much to a difference in the rate of profit.

When physical capital cannot be represented in a technical unit (a meccano set or a length of time) we have to resort to some other method to separate, as Professor Swan puts it, the “productive” from the “financial” element in the difference between two stocks of capital. This is what my system.of analysis is intended to do. To place the two economies in my scheme we need to know the technical conditions, which are in common, and the value of capital per head and the real wage rate in each economy. Exactly the same data are required to compile Professor Champernowne’s chain-index. I certainly do not “object” to anyone who pleases compiling the chain-index, since i t can always be taken to pieces again to show what is really happening, but its relation to the rest of the argument seems to be that of the fifth wheel on a coach.

Professor Swan finds my treatment of the rise in the degree of mechanization in discontinuous steps bizarre, though nowadays, in linear programming, it is quite familiar. What would continuity in the spectrum of techniques mean? It would mean that an indefinitely small rise in wages causes a rise in the degree of mechanization to be profitable. Consider any position where each producer is in equilibrium. Equilibrium means that the mar-linal returns on factors are propor- tional to their costs. One pound more per week spent on labour would save one pound per week of capital cost (the opportunity cost OP capital being a rate of interest equal to the going rate of profit). There are two techniques, one using a little more capital per man than the other, which give the same cost per unit of output. If one pound per week seems too coarse, make it one pound per year, or one shilling per year. However fine you make the division, there are always two techniques yielding the same rate of profit. When at a given wage rate Gamma and Beta techniques are equally profitable, an indefinitely small rise in the wage rate would make Beta and Alpha equally profit- able. I prefer to take a case where the required rise in wages is ihite, so that, for a somewhat smaller rise, only Beta technique would be eligible. This is not a matter of “realism”, but a device to enable us to see the relation between wages and techniques more clearly.

The reason why Professor Swan objects to this procedure is, I imagine, because he thinks of the wage rate as being determined by the physical marginal productivity of labour, which in turn is deter- mined by the amount of meccano in existence, so that a situation in which appreciably different wage rates are compatible with the same quantity of meccano fills him with consternation. But in his story, just as in mine, the rate of wages has to be such as to be compatible with full employment when the given rate of investment is going on. Professor Swan postulates that the technical conditions are such that the relative shares of wages and profits are independent of the level of wages (there is “unit elasticity of substitution”). This assumption

106 THE ECONOMIC RECORD APRIL

obviously could not hold good over ranges where there are large dis- continuities in the spectrum of techniques. But there is no reason to c o n h e the argument to the special case of constant relative shares, and since I suppose that he would agree that it is natural to assume that saving out of profits is greater than saving out of wages, he must agree that in equilibrium the level of wages is such as to make the dis- tribution of income such as to make full-employment saving equal to investment.

Given the propensities to save, the whole system is perfectly deter- minate whatever the technical conditions may be.

Professor Swan somehow suggests that the neo-classical condi- tions (marginal products equal to factor prices) and the Keynesian conditions (saving equal to investment at full employment) are mutu- ally exclusive, and take it in turns to determine the level of wages. If we could agree that equilibrium requires the Keynesian and the neo-classical conditions to be satisfied simultaneously, the whole con- fusion would be cleared up.‘

In any case, as Professor Swan says in a slightly different con- nection: “The multiplicity of explanations shows how treacherous is the idea of causation amongst interdependent variables.’’ It is never right to say that the marginal productivity of labour determines wages. All we can say is that, for a given marginal product of labour, equili- brium will obtain if the other conditions (in particular, the amount and form of capital in existence, the rate of investment and the pro- pensities to save) are such as to make the wage rate equal to it. If the other conditions make the wage rate Merent , the given marginal product is not compatible with equilibrium.

Another matter which puzzles Professor Swan is my attachment to the “Wicksell effect” or “absorption of saving” due to a rise in real wages. Here I must admit that in my first attempt to deal with the subject I caused some unnecessary confusion by a misleading use of language. I was treating of comparisons between equilibrium posi- tions, yet I talked about Wicksell and other LLeffects’l, which suggests a movement-time.5

4. A very simple but very important misunderstanding comes to light in the footnotes. Mr. Kaldor and I argue that in a static state, with zero net investment and no saving out of wages, profit on capital would be equal to the expenditure ot capitalists. Professor Swan regards this as a ham-and-eggs argument. Evidently he supposes that a capitalist cannot spend anything on consumption when he has no income. This is absurd. The capitalist does not even need to “dishoard” in order to consume. He commands credit at the shops. His orders raise demand, raise prices, generate profits, and, provided his fellows have been doing likewise, dividends come in in time to settle the bills. My endeavour is to reconale the Keynesian and the neo-classical theory, but Professor Swan insists on keeping them locked up in separate boxes.

5. In the mathematical part of his argument Professor Swan frequently makes use of small chungc~ in e.g. the wage rate as though equilibrium could instantaneously be re-established after such a change An equilibrium with a different wage rate entails a different past history. I t is of no use to “revalue” the stock of capital. If has to be completely re-created in the form appropriate to the new wage rate. (Even with the indestructible meccano, it has to be taken to pieces and reassanblcd.) To make the difference in wage rate “a small one” is the housemaid’s excuse. On the other hand as large a change in the stock of caqita! as can be made at a constant tnge rate may take place without disturbing equilibrium.

1957 GROWTH A N D CAPITAL ACCUMULATION 107

In connection with comparisons of equilibrium Professor Swan’s statement that “the Wicksell effect is nothing but an inventory re- valuation” has no meaning. In equilibrium, each economy has its own rate of profit. All the capital goods in existence in i t today were pro- duced with that rate of profit ruling, and the reproduction cost of each is equal to its historic cost. There was never a moment when any inventory had to be revalued. No change has ever taken place in the value of a stock of capital except the value of the change in that stock,6 and the economy with the larger value of capital must, over its history, have performed correspondingly more saving.

So much for the comparison of the two equilibrium points on Professor Swan’s diagram. To discuss a movement from one to the other is a much more complicated matter and if it is to be taken seriously we need to know a great deal more than he tells us-in par- ticular, what is the state of expectations in an economy when the rate of profit is falling as time goes by.

I will not attempt to rewrite his story, but only t ry to make clear what I understand by the Wicksell effect in this contest.

We may begin by borrowing Professor Swan’s indestructible and versatile meccano.

As the stock of meccano increases relatively to labour employed, real wages rise and the rate of profit falls. The wages cost of a new piece of meccano produced by an unchanged technique is therefore higher a t a later than an earlier date; the normal or “full cost” price of a new piece of meccano is not raised in proportion to the rise in wages, for the normal price has to be reckoned on the basis of the now lower normal rate of profit. The normal price of a new piece of mec- can0 may be less a t the later date, f o r the reduction in the interest element in its “full cost” may more than offset the rise in wages cost. (There is, of course, no reason to expect actual transactions to be made at normal prices while the economy is in a state of transition.)

Professor Swan calls the case where the normal price of a piece of meccano falls as the wage rate rises a “reverse Wicksell effect” whereas I prefer to keep the elements of cost separate and call only the change in actual wages cost a Wicksell effect. This is merely a matter of terminology.

At any moment the cost of a new piece of meccano has altered, since an earlier date, and existing meccano may be revalued accord- ingly. A rise in the value of the existing stock of capital (in the case where new meccano has risen in cost) is a pure matter of book-keeping, and cannot in any sense be said to “absorb saving” (though it does alter the amount of “waiting” that an owner of old meccano is doing -he must not treat the rise in its value as income and consume it). Professor Swan therefore seems to me to be completely off the rails when he identifies this revaluation with the Wicksell effect.

Now let us suppose that each piece of meccano has a limited Life. The new meccano being produced at any moment is not all net invest-

6. I must say that I take it father amiss that Professor Swan should think that I do not understand this distinchon.

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ment; part of it is replacement. It seems to me quite natural to speak of the excess of replacement cost over historic cost of a piece of mec- can0 as “absorbing saving”, and I should regard the Wicksell effect as being measured by the excess of the wages cost of the replacement at the date when it is made over what it would have been if the wage rate were still the same as at the date when this particular piece of meccano was constructed.

In any case, i t is the actual replacement cost of capital goods that matters. A ‘‘revaluation of inventories’’ neither absorbs savings nor provides fmance for replacement.

When we have to get on without the idea of pieces of meccano this simple way of dealing with the problem will not work. My scheme of analysis is intended to make it possible to discuss accumulation in spite of the fact that capital cannot be measured in physical units, but it is evidently not very easy to follow and I feel that I owe Professor Swan (and any other readers I may have) an apology for causing so much trouble. I can only plead that I was doing my best. It is not really my fault that capital does not consist of pieces of meccano.

Jom ROBINSON Cambridge.

AN AUSTRALIAN CONSUMPTION FUNCTION’

The favourite child of Keynesian econometrics, the consumption function, has everywhere let down its admirers. In Australia, the ratio of consumption to personal disposable incomes (at current prices) has varied in the post-war years between 79 per cent and 90 per cent. The year-to-year variations have been much too large to make this func- tional relationship a reliable tool for forecasting. Conversion of the function into real terms, with all the price-index snags which this en: counters, does not appreciably improve the situation. Can anythmg be done about this?

It has frequently been noticed that the variations in the ratio of consumption to personal disposable incomes in Australia are closely related to year-to-year fluctuations in the incomes of farmers. This appears to reflect a tendency of farmers not to adjust their current consumption expenditure to the large short-term fluctuations in their incomes. Perhaps the simplest hypothesis on these lines is to assume that consumption ( C ) is related, not to total personal disposable in- comes (PDI) but to non-farm disposable incomes (WDI).’

We are indebted to Dr. C. E. V. Leser, who kindly carried out the statistical computations for this note.

1. In either case, disposable income is here obtained by subtracting from income the relevant personal income taxes (excluding estate and gift duties)-in the one case all personal income taxes are subtracted to obtain PDI, in the other personal income taxes paid by the non-farm sector are subtracted to obtain NFDI.

No breakdown of personal income tax between farmers and non-farmers is published. Non-farm income tax for the post-war years has been estimated from data published in the National Incomr White Paper, the Reports of the Commissioner of Taxation, and (for 1954/5 and 1955/6) from the Commonwealth Budget Papers. It has been assumed that the shares of the two sectors in total income tax paid in