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Abstract
The present paper seeks to provide some new insights into the precise nature and the analytical foundations (or lack of them) of the familiar industry supply curve. We reconsider some fundamental phases of its historical evolution. Two different traditions are distinguished: one consists of the formalisations of Marshall's theory proposed by Barone and, later, by Pigou, Viner, Harrod and Robinson; the other consists of the models of Hicks and Allen, on the basis of ideas and criticism put forward by other London School of Economics scholars, like Kaldor and Robbins, in the mid-1930s. It is argued that the second tradition did not really remedy the weak aspects of the Marshallian theory of supply.
Acknowledgements
The authors thank two anonymous referees, Martin Currie, Christian Gehrke, Nerio Naldi and participants at a Manchester Metropolitan University seminar for helpful comments.
Notes
1 We make no claim to originality in this broad view. Raffaelli (Citation2003) presents a brilliant historical sketch of a ‘time-honored minority view’ that ‘recognize(s) that the direction taken by economic analysis in the 1930s unduly restricted the scope of Marshall's economics, without solving any of the major problems he had left open’ (2003: 1).
2 The manuscripts on value, published with extensive historical commentary by Whitaker (Citation1975 vol 1: 119–64), were probably prepared by Marshall for his ‘Tripos lectures’ at Cambridge in 1870 or so (Groenewegen Citation1995: 154–5). A more refined version belonged to the project of an early unpublished treatise on foreign trade, whose draft was nearly completed in 1875–7. The leading European economists saw Marshall's diagrams in two pairs of chapters, taken from the planned treatise and privately printed by H. Sidgwick in 1879, under the titles of The Pure Theory of Foreign Trade and The Pure Theory of Domestic Values (eventually published posthumous by the London School of Economics: see Marshall Citation1930). They soon became a sort of common knowledge, a shared acquisition, to the extent that some of them first reached the general public, with acknowledgments of course, in an Italian text, Pantaleoni's Principii di economia pura in 1889.
3 It cannot be seriously denied that Marshall developed his analysis of long-period supply much more fully than his short-period one. This prominence was ceaselessly stressed in Book V (cf. Principles: 403, and 377, 380, 382, 464), and it was plainly accepted by commentators. The MSS contain a distinction between four different lengths of time and emphasise the relevance of the longer ones; then the PTDV concentrated entirely on long (or very long) periods of time. For the purpose of this paper, then, we shall concentrate on Marshall's long-period curve.
4 For instance, in response to a permanent expansion of the fishing trade, ‘the industries connected with building boats, making nets, etc. being now on a larger scale would be organized more thoroughly and economically’ (Principles: 371). See also PTDV: 5–6.
5 See in particular Marshall's ‘A note on joint and composite demand’, in MSS: 160–164.
6 Very explicit statements can be found in Principles: 404.
7 In this respect, the controversial notion of the ‘representative firm’ is central. His taste for economic facts compelled Marshall to consider industries that comprise different firms: hence the necessity of some average, abstract representation (incidentally, in the PTDV and in the MSS, Marshall argued precisely in terms of an average of actual firms). Since, however, the long-run variety of firms was gradually given less and less emphasis in later literature on competitive supply, and since it is now often accepted that a long-period supply curve represents an industry formed by identical firms, we can put Marshall (as well as later authors) ‘on a par’ with the current treatment of the subject, ignoring any specific problems arising from the variety of firms. The reader is therefore asked to remember that by a ‘firm’ we do not mean here Marshall's representative firm or even an average firm proper, but the firm whose replication forms the industry.
8 See the ‘Preface’ to the eighth edition of the Principles: xvi. In the English version of his Principii di economia pura, Maffeo Pantaleoni claimed that the supply price should be equal to marginal, rather than average cost: ‘in Prof. Marshall's diagrams the supply curve is a curve of expenses per unit in function of quantity produced. It may seem doubtful whether it is convenient to consider the intersection of such a curve with the demand curve. (…) For the uses to which it is put by Prof. Marshall, a curve of marginal expenses, or marginal cost in money might be preferable’ (Pantaleoni Citation1898: 192, n 1).
9 According to Pantaleoni, the specific contribution of Marshall's supply and demand curves consisted precisely in the relationship between the industry's output and the long-period price. The conception of a long-period price at a given level of production was the same as Ricardo's, in Pantaleoni's interpretation. As he put it: ‘Ricardo's theorem, according to which, under conditions of perfectly free competition, commodities susceptible of reproduction are exchanged in accordance with the ratio of the costs, necessitates our considering the cost of production as the index of the available amount of every commodity. This doctrine is summed up in (…) elegant theorems of Professor Marshall’ (Pantaleoni Citation1898: 190).
10 ‘To adopt any other course would lead us to mathematical complexities, which though perhaps not without their use, would be unsuitable for a treatise of this kind’. (Principles: 852)
11 Each function w i = w i (a i (Q) · Q) is itself called a ‘supply equation’.
12 In Barone (Citation1992: 34), the equation at the bottom of the page is nothing other than Marshall's equation, in different notation. In a footnote he adds that ‘sometimes [Marshall] explicitly says that he takes it [the product supply curve] to be the particular case in which there is no composite demand for the factor services that are required to produce that product; sometimes he does not mention this assumption. However, an astute reader should always be prepared to make this assumption’ (Barone Citation1992: 36).
13 The need to consider a group of industries and simultaneous equilibrium in the case of composite demand had been envisaged by Marshall in the MSS. See the equations on MSS: 164.
14 In what follows, we have slightly changed Barone's notation, for reasons of consistency.
15 Called the ‘standard of utility’, by Barone.
16 This assumption is coherent with Marshall's idea ‘that the ordinary demand and supply curves have no practical value except in the immediate neighbourhood of equilibrium’ (Principles: 384 n.2; see also PTDV: 5).
17 See also Pigou (Citation1929: chapter XI of Part II and Appendix III).
18 In order to avoid the controversies that surrounded Marshall's concept of the ‘representative firm’, Pigou actually referred all of the argument to what he calls the ‘equilibrium firm’– a conception that made no impact in later literature!
19 Unfortunately Pigou did not quote Barone; he referred directly to Marshall's Principles, without any explicit consideration of other authors (with the exception of Chapman and Ashton).
20 Viner ‘maintained, explicitly or implicitly, that under long-run static competitive equilibrium marginal costs and average costs must be uniform for all producers’ (1953: 222), any difference in efficiency being ‘compensated by differential rates of compensation to the factors responsible for such differences’ (Viner Citation1953: 201). Since, however, he made almost nothing of such long-run differences, we may safely refer his argument to the case of identical firms, as we have done for the other authors.
21 Curiously enough, the original article contained the famous error originating precisely in the failure to draw the envelope of short-run cost curves properly, as Viner recognised in the 1953 Supplementary note (Viner Citation1953: 227).
22 ‘The procedure which will be followed, will be to begin in each case with the mode of adjustment of a particular concern to the given market situation when the industry as a whole is supposed to be in stable equilibrium’ (Viner Citation1953: 200; emphasis added).
23 Viner presented a similar taxonomy with reference to the firm's scale of production and to internal economies/diseconomies. This taxonomy, however, is of secondary importance for the supply curve: in fact, in the long period, the firm always operates at the bottom of its long-period average cost curve and by the Wong–Viner theorem both the plant and the output are uniquely determined.
24 He then refers to ‘cross-fertilization’ and ‘exchange of ideas’ as factors that ‘appear to be possible sources of technological external economies resulting from an increase in the size of the industry as a whole’ (Viner Citation1953: 218).
25 This point has been developed analytically in Opocher and Steedman (Citation2008).
26 Samuelson traces this lack of distinction back to Walras's assumption of constant returns to scale. See Samuelson (Citation1947: 79).
27 See Walras (Citation1969 [1896: Lesson 22 and in particular Figure 24).
28 Cf. Kaldor (Citation1934: 60) and Hicks (Citation1934: 237). Offer as negative demand was also a major feature of Wicksteed's theorising. Marshall noted that the symmetry of reciprocal demand curves he discussed in the Pure Theory of Foreign Trade was broken when passing to curves of supply and demand, which he discussed in the PTDV: see Marshall (Citation1930: 2).
29 Cf. Walras (Citation1969: Lesson 9, and in particular 139).
30 We note in passing that if the numéraire of the output price is a composite of inputs, the same curve (except for scale) is obtained irrespective of the weight given to each input, for the simple reason that all input prices are constant along the supply curve: no numéraire problem of the kind referred to in the previous section can possibly arise in this context.
31 Samuelson (Citation1947) was among the first to introduce profit and cost functions: see, in particular, 1947: 76–8. A complete formal theory of cost functions for the price-taking firm was first presented by Shephard (Citation1970).
32 ‘Nevertheless it does not appear that for our present purposes the qualifications introduced by the possibility of new firms are likely to be serious’ (Hicks 1948: 102).
33 ‘If no such fixed [productive] opportunity exists, then there is no reason why an equal proportional increase in all factors should not enable all products to be increased in the same proportion as the factors have been increased’ (Hicks Citation1946: 322).
34 ‘[I]n the long period, if all elements are variable and returns are constant (…) the prices assume particular given values and no one of them can be changed by itself without destroying equilibrium’ (Allen Citation1957: 617).
35 ‘If competition is “pure” in the commodity and factor markets, and the production function is homogeneous of the first order, then it is a classical fact that (…) the Hessian of the production function is singular. Therefore a regular maximum for the firm is impossible’ (Samuelson Citation1947: 78).
36 See Silberberg (Citation1974a, Citation1974b) and the references therein quoted.
37 Silberberg, for example, changed both one input price and the product price, so as to keep profits equal to zero, and examined the consequent changes in input use per unit of output.
38 Taking these effects into account makes a difference to the comparative static properties of equilibrium (‘full equilibrium’) of the competitive firm, as Steedman (Citation1998) has shown.
39 A very clear example of this ‘double’ conception of the long-run equilibrium of the firm is in Henderson and Quandt (Citation1971: 111 and 117, respectively).
40 See Walras (Citation1969: Lesson 22, Figure 24(a), 262).
