Interpreting the "representative firm"

Marshall's notion of the representative firm is an idea I have never really understood. But, to be fair to me, I'm not sure anyone else understands it either. Take, for example, Michel Quere (Quere 2006) who has written

The representative firm is a key analyical device in Marshall's Principles of economics.

and compare this with Lionel Robbins's view that the representative firms was,

Conceived as an afterthought ... it lurks in the obscurer corners of Book V [of Marshall's Principles] like some pale visitant from the world of the unborn waiting in vain for the comforts of complete tangibility.

Its difficult to see how the notion can be both a key device and a pale visitant from the world of the unborn.

In fact it was Robbins along with Piero Sraffa who are largely to blame, or who deserve most of the credit, for the controversy that lead to the replacement of the representative firm with Pigou's equilibrium firm.

One of the problems with the representative firms is that it has at  least two interpretations. Quere writes,

On the one hand, long-run equilibrium and free competition have been mainly associated with static equilibrium and perfect competition. In line with this interpretation, Sraffa [...] demonstrated the inconsistency of the representative firm as an equilibrium firm, due to the role played by internal and external economics. However, as became clear afterwards, the originator of the representative firm as an equilibrium firm was Pigou [...] and not Marshall [...]. To put it more precisely, increasing returns (resulting in economics of production on a large scale) are incompatible with the requirements for the supply curve. Their effects are either too wide or too restricted. For example, internal economics can be seen as excessive because they rapidly become incompatible with competitive conditions. On the other hand, external economies are inconsistent with the conditions of the particular equilibrium of one commodity. In order to be compatible with the laws of returns, the representative firm requires a very particular context, namely one in which external economics are 'those economics which are external from the point of view of the individual firm, but internal as regards he industry in its aggregate' [...]. But that context is likely to be rather useless as 'it is just in the middle that nothing, or almost nothing, is to be found'[...]. Therefore, the likelihood of supply curves showing decreasing costs can only be very low. Moreover, Robbins [...] complemented Sraffa's attack by showing that the concept of a representative firm was inappropriate to a proper distribution theory, and very misleading. Thus, when Keynes arranged for the 1930 symposium, this interpretation of the theory of the representative firm was brought to an end, despite Robertson [...] - and, to a lesser extent. Shove's [...] attempt at a defence. In the end the symposium fully legitimated the importance of a framework of monopolistic competition.

So by around 1930 Marshall's representative firm was no longer represented in economic theory.

But in the 1950s there was a renewal of interest in the idea. But with this new interest came a new interpretation of the notion. Here the representative firm is seen as a device to blend theory and facts in a proper fashion. Quere again,

First, the representative firm is a central device for bridging the contents of Book IV and Book V of the Principles. It also has a pivotal role in reconciling static equilibrium and evolution [...]. Second, thanks to the representative firm, an industry supply price can be downward-sloping but compatible with equilibrium, as the supply curve is not expressing the marginal costs of production for various firms in the industry, but 'the prices at which particular quantities demanded will be supplied in equilibrium' [...]. In other words, 'marginal' cost in Marshall's wording is something to be applied to aggregate values; that is, to the shape of the supply curve for the whole industry. It is a means of expressing the fact that cost lies on the marginal short-period cost curve but is conditional to any movement along the long period unit cost curve. As pointed out by Frisch [...], Marshall focused his attention much more on the nature of marginal production than on that of marginal cost. Therefore, a marginal cost curve for the individual firm is not meaningful. With the representative firm theory, Marshall was providing the best approximation he could find to solve the difficulty of making long run evolution compatible with equilibrium analysis.

Third, beyond the issue of costs, the representative firm theory also expresses the need to deal with the structure of industries. This is where I think Marshall's economics is still very relevant. With respect to this, it is especially essential to highlight two central issues: one is the heterogeneity in the organization of industries, the other is the importance of market imperfections with regard to the dynamics of industries.

The representative firm theory legitimates the importance of the concept of industry, which can he defined as a set of producers, a group of various firms significantly affected by any decision of one of them [...]. Wolfe insists on the usefulness of that Marshallian definition, which frames 'a theory [of the structure of industries] much more complete than any competitor' [...]. Moreover, the representative firm theory is a means of reflecting about the variety of firms' behaviour and performance (weak, average, strong) within an industry. Due to internal economics, firms in the same industry do not command the same technological and organizational resources. The representative firm theory is therefore an attempt to take into better account not only the structural variety among producers hut also their various reactions to changes and shocks in their environment. Both differ substantially from industry to industry: the representative firm theory is a means of expressing how industrial contexts are differently organized, sensitive, and reactive to shocks. By doing so. Marshall provides the best possible way of applying his constructive work philosophy lo the problem of the organizational diversity of industries.

The second issue is the importance to be given to 'market imperfections', to use the modern phrase. Free competition requires that internal economics do not lead to a permanent monopoly. This is only possible because of the twofold importance of innovation and market imperfections. Innovation brings about the weakening of temporary monopolies, but this point is not really considered in Marshall's analysis, which is mainly concerned with 'limited dynamic change' [...]. But a free competitive context also requires the existence of market imperfections; that is, of all kinds of frictions in the working of markets. Without the latter, an individual firm experiencing increasing returns would come to monopolize the whole market and increasing returns would then be incompatible with competitive equilibrium. Connections between producers (taking care of a whole 'supply chain oligopoly') are very influential in determining the price that will prevail at equilibrium. Now, if market imperfections are essential for understanding Marshall's dynamics, their critical importance cannot be really acknowledged within the frame of the Principles, at least with regard to the representative firm theory. Finally, despite the richness of the latter, one has to remember the prominence of Marshall's machinations at Cambridge to establish economics as a profession, and the role played by the Principles in establishing marginalism as the dominant paradigm.

While there was this renewal of interest in the representative firm it largely came to nothing. The mainstream theory of the firm remained the equilibrium firm up until the 1970s (and in textbooks even to today) when the Coaseian approach to the firm began to be developed by people like Oliver Williamson.

So what is the representative firm? Damned if I know. But even if I did I'm not sure it would matter for understanding the modern theory of the firm.

Ref.:

• Quere, Michel (2006). 'The representative firm'. In Tiziano Raffaelli, Giacomo Becattini and Marco Dardi (eds.), The Elgar Companion to Alfred Marshall (pp. 412-7), Cheltenham, U.K.: Edward Elgar.