254. Harrod to D. H. Robertson , 3 September 1932 [a]

[Replies to 253 , answered by 255 ]

Marine Hotel, Crail, Fife 1

3 September 1932

My dear Dennis

I hope I havent given you too much "heart" about the book. [1] I wrote probably in a mood of optimism. About foreign investment--I wonder what lines you are thinking on. Is your review in the Sept. no. of E.J.? [2] I havent seen Abbati's book yet. Is it a theoretical, statistical, historical or descriptive treatment you are thinking of? I too feel this is a lacuna, but am not quite sure on what lines to go.

If, when I look at the typescript again, it seems to me any good, I surely ought to be able to finish off this autumn? I will let you know again, certainly before next term. I enclose a list of chapter headings (tentative).

Now with regard to your note. [3] I will keep the typescript a little longer, if you dont mind. I have written out the enclosed in the hope that it may move you! It is about your section 4 (case 2) [4] which touches me most nearly.

I was very interested in what you wrote about demand being in some sense implicit in the ordinary cost curve. [5] But I still think that marketing expenses give rise to a special problem, not covered by the ordinary notion of the adaptation of an industry to its scale of output, and that in tackling this problem we may make an advance towards explaining how decreasing costs are consistent with the equilibrium of individual firms in competition. [6] What I feel about your sec 4 [7] is that it may be formally correct but is a little vague or, shall we say, general in wording, and that it tends to obscure a real vital difference, that has been established, in the interests of a merely formal uniformity. It might also convey to the mind of the reader that in spite [b] of recent attempts at analysis, things are really precisely where they were before with regard to the possibility of equilibrium and decreasing costs. I dont know if you mean to convey that impression. If you do, I believe that it is because I have failed to convey my meaning and not because what I do mean is mistaken or really leaves things where they were. If you dont mean to convey that impression, then I think you ought to add that of course there are important differences in the relation of the cost curve to the demand curve according to whether marketing expenses are or are not present.

Allen of London had a short note in the last E.J. about my article and applied certain formulae to the problem. While acknowledging that the result I claim was possible, he held that marketing expenses must be "large" to yield this result. He has however made some mistake or got into some muddle in interpreting his own symbolism. I have gone over his ground again in a note which I hope will appear in the next E.J. and shown that his formulae if properly interpreted yield precisely my result. [8] Do look over this if it appears. It seems to me to place this particular conclusion on a very solid foundation.

I hope my note on the back of p. 4 enclosed [9] may bring out the essential point as clearly as anything. But what feeble tools words seem to be.

I hope you will enjoy Ireland. I am at present at the seaside with my mother here. It is quite agreeable [c] but not very fine.

Yours

Roy

1. You say "in both cases it is assumed that the industry is adapted to the scale of output." [10] Is it quite right to say this of the second case? If individual sources are each subject to decreasing costs and competitive marketing expenses, then surely the whole industry is not adapted to its scale of output; there are too many sources of supply.

As, however, our problem is with the equilibrium return the supply of the individual source and the demand for its output, we may get something of what you want by saying that each source, or the equilibrium source, is adapted to its scale of output. (This presumably means that fixed and liquid productive resources are mixed in the optimum proportions for each amount of output).

2. Now it is perfectly true that you can draw to cover case 2 a supply (or cost) curve in two dimensions showing the cost of production of each amount assuming that the source is in each case adapted to produce the amount it does produce. It remains to ask what, having drawn such a curve, you expect to get from it. Those curves are intended not to be objects of beauty only but to yield information. In particular they are expected to yield information (i) about the conditions of equilibrium and (ii) about what will happen to costs when demand is expanded or contracted.

Consider your curve with reference to (i). The particular demand is a horizontal st[raight]. line and the cost curve is falling. 2   [11] At the point of intersection the cost curve will be dropping below the demand curve. This is not a condition of equilibrium. Thus your curve fails in case 2 to show how equilibrium is established. Yet the demand and supply curves together are usually expected to show just that.

It seems to me that it is not enough to show that in case 2 a curve can be constructed in the manner you indicate, [12] but that we also want to know whether that curve will demonstrate the conditions of equilibrium and, if not, what kind of construction must take its place.

In case 1 the problem does not arise, because the cost curve must be rising at equilibrium. It will be present to your mind that the whole of this analysis is an attack on the problem of how equilibrium is possible with decreasing costs, having regard to the position of the equilibrium firm. Your construction does not show why, in case 2, the equilibrium firm does not expand output, as it would do if, in the conditions of case 1, the cost curve was declining.

By assimilating the construction in case 2 to that in case 1, you seem to cover up and hide the essential circumstance which leads to the possibility of a result, viz. decreasing costs, in case 2, which is impossible in case 1.

3. Ah, you may say, but this cost curve is a long period affair (showing costs when the firm is adjusted to its output) and isnt expected to demonstrate the conditions of short period equilibrium; the short period cost curve is of course ascending. But this will not do. According to me both the short and the long period cost curves may be descending, when the firm is adjusted to the output it is producing. (cf. my construction of the family of curves and the envelope; [13] a similar construction was also worked out independently by Viner, tho' he got an essential detail wrong. [14] ) If both long and short curves are descending and the demand is horizontal, your construction simply fails to show how equilibrium is established.

You may say, well, I dont care; I shall construct my curves in this way all the same. You are entitled to. But you should add a footnote that in case 2 the intersection fails in a very important respect in which it is successful in case 1, viz. it does not show the condition of equilibrium. Such a footnote re-introduces in another form the difference between cases one and two, which your use of the same curve for both has tended to conceal.

4. A note on what you say about the curve representing the cost of producing x for all values of x, when the "industry", but we must now substitute "source of supply", is adapted to each value of x (each scale of output). [15] Surely this "adaptation" consists of regulating the amount of fixed plant present in relation to the amount of liquid resources applied to it. Now it is quite possible in case 2 that as demand expands and output expands no re-adaptation is necessary. Nay it is not only possible but in a certain sense it is probable. It may happen that as all productive resources are employed on a larger scale, fixed as well as liquid, costs per unit fall. The optimum proportions for the smaller scale may be the same as the optimum proportions for the larger scale. You might object--"but I call this increase of fixed plant in proportion to the increase of liquid resources and adaptation". I put in another case: it might happen that for any output between x 1 and x 100 the same amount of fixed plant gives the optimum result, e.g. you use the best machinery available, the minimum unit of it producing x 100 , but it also being worth while to use it for x 1 .Then if normal output rises from x 50 to x 51 , no increase of fixed plant is required. None the less if there are marketing expenses the firm is in equilibrium at one cost for x 50 in a given state of demand, and at a lower cost for x 51 in another state of demand. There has been no adaptation to the new state of demand whatever. The rise of demand has simply caused output to expand and total cost to fall.

5. Now consider the second purpose that the cost curve is supposed to secure (vid. sup) namely to show what will happen if demand changes. You claim to represent the situation in this figure:--[fig. 1] 3 [16]

Your maxim for determining equilibrium must be "take the point of intersection." To that I insist on adding: "and see that the cost is not falling below demand at that point." If you add my maxim your construction becomes impotent. But suppose we accept your position and confine ourselves to your maxim. What happens when there is a rise of demand? [fig. 2] The new point of intersection is to the left of the old, output will be contracted and the cost will rise. This is clearly nonsense. And the consequences are worse. For if the equilibrium firm contracts output, the price will rise still further than was due to the original rise in demand and output will be further contracted. Thus it seems to me that your construction fails to fulfil either of its proper functions.

The source of what I believe to be your mistake is in the confusion between the effect of a change in demand on costs indirectly thro' changing the optimum lay out of the plant and that on costs directly thro' changing marketing expenses. The first (indirect) effect is already taken account of in the Pigouvian [d] supply curve, [17] but not the second (direct) effect.

6. However we look at it, the ordinary curve takes cost to be a function of amount produced only. There being only two dimensions, and one being used for the cost itself, the other is used up to represent amount. Now if we are convinced that in fact cost is a function of two independent 4 variables, amount of output and "state of demand", we must require more than two dimensions. However we play around with language we cannot get over this simple mathematical fact.

  1. 1. Harrod, International Economics ( 1933:10 ).

    2. D. H. Robertson, "The Economic Lesson of 1929-31: The First Eleven Bulletins of the Unclaimed Wealth Utilisation Committee of Geneva, Under the Chairmanship of A. H. Abbati", Economic Journal XLII, December 1932, pp. 612-14.

    3. D. H. Robertson, "A Note on the Supply Curve", Ts, 10 numbered pages plus cover page, not published, in DHR C18/8 (6-16). The note regards the recent literature on "the theory of equilibrium under conditions of polipoly and decreasing cost", and in particular Harrod's "The Law of Decreasing Costs" ( 1931:2 ).

    4. Robertson discusses three cases:

    • (1) The case of perfect competition. (2) A case in which the individual firm, working under conditions of decreasing cost in respect of its manufacturing expenses, is prevented from expanding its sales, at a price determined in the general market, by the heavy marketing expenses which it would have to incur to attract trade from its rivals: but in which an expansion in the whole industry will enable it to expand its market without incurring such expenses and thus to reap the advantages of decreasing manufacturing costs. (3) A case in which heavy initial outlay has to be incurred by a firm in order to produce any output at all, but the cost of additional output is small (pp. 1-2).

    5. With respect to case 3 (see note 4 to this letter), Robertson noted that firms are equipped to produce from the start very large output, but are restricted by the inelasticity of their particular demand curve: "I doubt whether it is possible to frame for this case a definition of supply price without explicitly mentioning state of demand, as distinct from merely scale of output". However, he concluded: "But that does not mean that the supply curve is not independent of the demand curve, and properly to be drawn on a plane surface." (pp. 6-7)

    6. See in particular Harrod, "The Law of Decreasing Costs" ( 1931:2 ), pp. 567-68 and 572.

    7. In criticizing Harrod's claim that in the presence of marketing expenses the supply price is a function not only of the quantity of output, but also of the state of demand (Harrod, "The Law of Decreasing Costs", pp. 568 and 572), Robertson argued as follows:

    • The fact that price now depends on scale of total output for a new reason, viz. because an increase in the scale of output lowers competitive marketing as well as (or instead of) other sorts of costs, does not serve to differentiate this case, from the present standpoint, from the case of perfect competition. In both cases it is assumed that the industry is adapted to the scale of output, which is the same thing as saying that it is adapted to the state of demand: and in both cases there is a unique relation between scale of output and average cost of production. Mr Harrod, perhaps not having noticed the ghost of demand curves in the background of case (1), is unduly alarmed at their appearance in case (2), and is led into asserting a functional dependence of supply price on demand curve which in this case does not--or at all events need not--exist.

    8. R. G. D. Allen, "Decreasing Costs: A Mathematical Note" Economic Journal XLII, June 1932, pp. 232-36. Harrod, "Decreasing Costs: An Addendum" ( 1932:6 ).

    9. Reproduced as footnote to [jump to page] .

    10. The passage is quoted in full in note 7 to this letter.

    11. The purpose of Harrod's article was to demonstrate the possibility of competitive equilibrium with decreasing costs, while Robertson enquired whether, where decreasing costs prevail, it is possible "to draw up a long-period supply curve which is a proper denizen of a two-dimensional surface,--a true hypothetical curve, really independent of the demand curve and fit to be yoked with it as co-blade of a pair of Marshallian scissors" (p. 1).

    12. Case 2 is characterized by decreasing costs (see note 4 to this letter), as well as case 3; the latter, however, is represented by something like a rectangular hyperbola. Robertson did not supply any diagrams, nor indicated how a diagram should be constructed; he explained, however, that it corresponds to the celebrated case of the medal-making industry as discussed by H. Cunynghame, Geometrical Political Economy (Oxford: Clarendon Press, 1904; the case is not mentioned in Harrod's reading notes, in HP V-41. Harrod's copy of the book is in HCN Roybooks), pp. 54-55, and Pigou, "The Law of Diminishing and Increasing Costs", Economic Journal, June 1927, pp. 194-95. Harrod represented Robertson's case 2 as fig. 1.

    13. Harrod, "The Law of Decreasing Costs", p. 575.

    14. J. Viner, "Cost Curves and Supply Curves" (1931). The diagram is on p. 35. On Harrod's criticism to Viner's curve see note 6 to letter 227 , [jump to page] .

    15. The passage is cited in note 7 to this letter.

    16. The figure was not explicitly drawn by Robertson: see note 12 to this letter.

    17. A. C. Pigou, "An Analysis of Supply" (1928). In his paper, with reference to pp. 238-39 of Pigou's article, Robertson pointed out that the state of demand enters the notion of the quantity a firm is adapted to produce, on which its supply-price corresponding to any quantity of output is calculated ("A Note on the Supply Curve", pp. 3-5).

    1. a. ALS, two pages on one leaf, plus note, five pages on four numbered leaves (the last being written on both sides); in DHR C18/7(1-5).

      b. Ms: «inspite».

      c. Ms: «agreable».

      d. Ms: «Pigovian».


1. "but Ch. Ch. Oxford find me" [Harrod's note].

2. not the curve of corresponding monetary cost [Robertson's pencilled note in the margin].

3. No! DHR (Robertson's pencilled comment in the margin).

4. The use of the word independent here is vital, vital both to secure my conclusion mathematically and to interpret the economic facts correctly. It also differentiates between the case in which demand may be implicitly represented in the cost curve and where it may not. The amount of output no doubt depends on demand; productive costs depend on amount of output and \ indirectly on state of demand. Thus making cost a function of amount of output makes it indirectly a function of state of demand. But marketing costs unlike productive costs depend on state of demand directly and this dependence is not mediated by the amount of output. Thus the marketing cost of the same amount of output, x 0 , will change if the state of demand changes. This proves that the influence of the state of demand on marketing cost is not mediated by amount of output. \ we must take state of demand as an independent variable of which cost is a function directly. It may also be a function of state of demand indirectly via the other variable. Per contra a change in the state of demand will have no effect on productive cost, if there is no change in output. Consequently where there are no marketing costs (as in case one) the need for a second independent variable is eliminated, all variations in the state of demand necessarily acting through the variable you already have, viz. quantity of output. But this is not so in case 2. [Harrod's note on verso of p. 4].


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