Arrigo Opocher & Ian Steedman (2008) The industry supply curve:
Two different traditions, The European Journal of the History of Economic Thought,
Marshallian Tradtion considered equilibrium of industry as a whole, There are heterogenous firms within the industry, at different stages of growth. Their "equilbrium" may not be well defined, but in any case depends on the whole industry. The industry supply is not a partial equilbrium concept -- rather, as we move on it, everything else changes at the same time.The supply just captures two variables. The supply curve could take many different shapes, increasing decreasing or a mixture, because of the general equilbrium effects -- returns to scale due to expansion of industry. Barone noted that these interdepencies may cause indeterminacy of the supply curve -- the price of a given quantity supplied may depend on the OTHER industry supplies. Let q be the output of the firm and Q that of the industry. Than the inputs K,L,E,M used to produce q are a function of Q the total industry output. ALSO the price of these inputs (w,r, etc) is a function of Q. Thus total output of industry determines both factor prices and factor proportions in production for a given firm.
Marshall’s supply curve, was essentially based on ‘external’ effects, such as changes in input prices
or changes in technological efficiency due to a varying industry output. The Industry is the primary object of analysis:
cost conditions in the individual firm (i.e. costs as a function of the firm’s output) and the equilibrium size of the firm were, in fact, dependent upon
the industry’s output. In this sense, their very conception of the firm was dependent on their conception of the industry.
Kaldor (1934) explicitly attacked the Marshallian tradition in the very pages of The Economic Journal where Marshall’s theory
of supply had been presented, criticised and developed:
(Marshall & his followers) constructions suffer from the same deficiency as Marshall’s. (. . .) Explicitly or implicitly, the equilibrium
of the ‘firm’ is made dependent upon the equilibrium of the ‘industry’ rather than the other way round. (Kaldor 1934: 63)
Quite to the contrary, Kaldor says, it was: necessary to analyse the conditions of equilibrium for the individual firms before any
postulates were made about the supply-function of an industry. (. . .) Only then can we derive those supply curves of various shapes which the simple two-dimensional
diagram at once suggests to the mind. (Kaldor 1934: 61; emphasis added)
Kaldor pleaded for an extension and adaptation of general ideas of price-taking behaviour to the specific field of product supply. This
proposed micro-foundation of the supply curve was naturally extraneous to all kinds of external effects (see Kaldor 1934: 66), and in particular to input
price changes: the object of study became the reaction of individual firms and of the industry to a parametric change in the price of the product alone,
taking all other prices as constant by definition.
simple case of a single product firm ðw; pÞ ! ðx; qÞ: In order to represent this mapping (when it exists) with functions of one
variable, all other variables have to be taken as constant by assumption. If all input prices are assumed constant, we end up with output and input use as
functions of the output price. In the (q, p) space, this is the supply curve of the firm
By the very logic of profit maximisation, then, the short-run supply curve of the firm slopes upward, quite independently of any empirical consideration. The results obtained for the firm immediately generalise to the industry’s short-run supply curve. In the words of Hicks:
Strictly speaking, we only discussed in the last chapter the effect of a change in price on the demands and supplies of a single firm. Here we need the effect on a group of firms. For the most part this effect can be got by aggregating the effects on single firms, as we found we could aggregate the effects on private individuals; so far the group must obey the same laws as the single firm. (Hicks 1946: 102; emphasis added) On the contrary, the passage from the short period – where the new approach found its most natural application – to the long, encountered a series of problems. In fact, Hicks goes on to ask: What happens, however, if the change in prices has the effect of altering the number of firms producing a particular commodity, so that firms enter or leave the ‘industry’? This is a notoriously tricky matter, and it is right that we should proceed with caution.
(Hicks, 1946, p. 102)
It is not possible for the price of one factor (or product) to change, there being no change in the prices of all other factors and products, without upsetting equilibrium altogether. If the price of a product rises, output would become infinite; if the price of a factor rises, it will become zero. In the limiting case we are considering, our analysis threatens to break down altogether. (Hicks 1946: 322)
If one industry expands, other industry must contract, since they use the same resources.
FINAL SECTION: How do textbooks deal with these problems?
Conclusion not satisfactorily.
One approach has positive profits in the long run Then the question is: what happened to free entry.
Other approaches have constant long run costs -- this makes scale indeterminate.
If costs of inputs rise as production increases, then this must impact on other sectors, and so partial equilibrium cannot be suitable analysis.
None of these problems are resolved in current textbooks