Partial versus general equilibrium: the theory of the firm example

A point worth making about the modern models of the theory of the firm is that they illustrate a general issue to do with post-1970 microeconomics, namely, the retreat from the use of general equilibrium (GE) models.

Historian of economic thought Roger Backhouse writes that

 “[i]n the 1940s and 1950s general equilibrium theory [ ...] became seen as the central theoretical framework around which economics was based” (Backhouse 2002: 254)

and that by the

“[ ...] early 1960s, confidence in general equilibrium theory, and with it economics as a whole, as at its height, with Debreu’s Theory of Value being widely seen as providing a rigorous, axiomatic framework at the centre of the discipline” (Backhouse 2002: 261), 

but

“[ ...] there were problems that could not be tackled within the Arrow-Debreu framework. These include money (attempts were made to develop a general-equilibrium theory of money, but they failed), information, and imperfect competition. In order to tackle such problems, economists were forced to use less general models, often dealing only with a specific part of the economy or with a particular problem. The search for ever more general models of general competitive equilibrium, that culminated in Theory of Value, was over” (Backhouse 2002: 262).

As early as 1955 Milton Friedman was suggesting that to deal with “substantive hypotheses about economic phenomena” a move away from Walrasian towards Marshallian analysis was required. When reviewing Walras’s contribution to GE, as developed in Walras’s famous Elements of Pure Economics, Friedman argued,

“[e]conomics not only requires a framework for organizing our ideas [which Walras provides], it requires also ideas to be organized. We need the right kind of language; we also need something to say. Substantive hypotheses about economic phenomena of the kind that were the goal of Cournot are an essential ingredient of a fruitful and meaningful economic theory. Walras has little to contribute in this direction; for this we must turn to other economists, notably, of course, to Alfred Marshall” (Friedman 1955: 908).

By the mid-1970s microeconomic theorists had largely turned away from Walras and back to Marshall, at least insofar as they returned to using partial equilibrium analysis to investigate economic phenomena such as strategic interaction, asymmetric information and economic institutions.

All the models considered in this book are partial equilibrium models, but in this regard, the theory of the firm is no different from most of the microeconomic theory developed since the 1970s. Microeconomics such as incentive theory, incomplete contract theory, game theory, industrial organisation, organisational economics etc, has largely turned its back, presumably temporarily, on GE theory and has worked almost exclusively within a partial equilibrium framework. This illustrates the point that there is a close relationship between the economic mainstream and the theory of the firm; when the mainstream forgoes general equilibrium, so does the theory of the firm.

One major path of influence from the mainstream of modern economics to the development of the theory of the firm has been via contract theory. But contract theory is an example of the mainstream’s increasing reliance on partial equilibrium modelling. Contract theory grew out of the failures of GE. As Salanie (2005: 2) has argued,

“[t]he theory of contracts has evolved from the failures of general equilibrium theory. In the 1970s several economists settled on a new way to study economic relationships. The idea was to turn away temporarily from general equilibrium models, whose description of the economy is consistent but not realistic enough, and to focus on necessarily partial models that take into account the full complexity of strategic interactions between privately informed agents in well defined institutional settings”.

The Foss, Lando and Thomsen classification scheme for the theory of the firm clearly illustrates the movement of the current theory of the firm literature away from GE towards partial equilibrium analysis. The scheme divides the contemporary theory into two groups based on which of the standard assumptions of GE theory is violated when modelling issues to do with the firm. The theories are divided into either a principal-agent group, based on violating the ‘symmetric information’ assumption, or an incomplete contracts group, based on the violation of the ‘complete contracts’ assumption. The reference point approach extends the incomplete contracts grouping to situations where ex-post trade is only partially contractible.

The introduction of the entrepreneur, as in the models proposed by Silver, Spulber and by Foss and Klein, also challenges, albeit in a different way, the standard GE model since, as William Baumol noted more than 40 years ago, the entrepreneur has no place in formal neoclassical theory.

“Contrast all this with the entrepreneur’s place in the formal theory. Look for him in the index of some of the most noted of recent writings on value theory, in neoclassical or activity analysis models of the firm. The references are scanty and more often they are totally absent. The theoretical firm is entrepreneurless−the Prince of Denmark has been expunged from the discussion of Hamlet” (Baumol 1968: 66).

The reasons for this are not hard to find. Within the formal model, the ‘firm’ is a production function or production possibilities set, it is simply a means of creating outputs from inputs. Given input prices, technology and demand, the firm maximises profits subject to its production plan being technologically feasible. The firm is modelled as a single agent who faces a set of relatively uncomplicated decisions, e.g. what level of output to produce, how much of each input to utilise etc. Such ‘decisions’ are not decisions at all, they are simple mathematical calculations, implicit in the given conditions. The ‘firm’ can be seen as a set of cost curves and the ‘theory of the firm’ as little more than a calculus problem. In such a world there is a role for a ‘decision maker’ (manager) but no role for an entrepreneur.

The necessity of having to violate basic assumptions of GE theory so that we can model the firm, suggests that as it stands GE can not deal easily with firms or other important economic institutions. Bernard Salanie has noted that,

“[ ...] the organization of the many institutions that govern economic relationships is entirely absent from these [GE] models. This is particularly striking in the case of firms, which are modeled as a production set. This makes the very existence of firms difficult to justify in the context of general equilibrium models, since all interactions are expected to take place through the price system in these models” (Salanie 2005: 1).

This would suggest that to make GE models a ubiquitous tool of microeconomic analysis - including the analysis of issues to do with non-market organisations such as the firm - developing models which can account for information asymmetries, contractual incompleteness, strategic interaction, the existence of institutions and the like is not so much desirable as essential. One catalyst for the development of such a new approach to GE is that partial equilibrium models can obscure the importance of the theory of the firm for overall resource allocation, a point which is more easily appreciated in a GE framework.

Changes in economic theory

This piece by Justin Fox at BloombergView is just one example of the increasing discussion of the move towards empirical work, away from theory, in economics. This table from Hamermesh (2013: 168) shows the changing nature of research in economics: the amount of theory being published is decreasing while the amount of empirical/experimental work is increasing.

But what is missing from this discussion, however, are the changes in theory that have taken place as well. Since, roughly, 1970 the nature of the theory that is being done has changed. To quote me, Walker (2016: 155):

A final point about the models of the firm discussed in this book is that they highlight a general issue to do with post-1970 microeconomics; namely, the retreat from the use of general equilibrium (GE) models.

Much of the modern theory has developed as a reaction to perceived failures in the standard general equilibrium theory. As Salanie (2005: 2) has argued for the case of contract theory:

The theory of contracts has evolved from the failures of general equilibrium theory. In the 1970s several economists settled on a new way to study economic relationships. The idea was to turn away temporarily from general equilibrium models, whose description of the economy is consistent but not realistic enough, and to focus on necessarily partial models that take into account the full complexity of strategic interactions between privately informed agents in well-defined institutional settings.

What is interesting about the these changes is that they consist of a move not towards a new general equilibrium theory but rather a movement back to partial equilibrium models.

As early as 1955 Milton Friedman was writing,

Economics not only requires a framework for organizing our ideas [which Walras provides], it requires also ideas to be organized. We need the right kind of language; we also need something to say. Substantive hypotheses about economic phenomena of the kind that were the goal of Cournot are an essential ingredient of a fruitful and meaningful economic theory. Walras has little to contribute in this direction; for this we must turn to other economists, notably, of course, to Alfred Marshall. (Friedman 1955: 908)

By the mid-1970s microeconomic theorists had largely turned away from Walras and back to Marshall, at least in so far as they returned to using partial equilibrium analysis to investigate economic phenomena such as strategic interaction, asymmetric information and economic institutions.

If we take as an example the theory of the firm one can clearly see this move away from general equilibrium. Foss, Lando and Thomsen (2000) offer a classification scheme to help understand the modern theory of the firm. The scheme divides the contemporary theory into two groups based on which of the standard assumptions of general equilibrium theory is violated when modelling issues to do with the firm. The theories are divided into either a principal–agent group, based on violating the 'symmetric information' assumption, or an incomplete contracts group, based on the violation of the 'complete contracts' assumption.

The necessity of having to violate basic assumptions of general equilibrium theory so that we can model the firm, suggests, importantly, that as it stands general equilibrium cannot deal easily with firms, or other important economic institutions. Bernard Salanie has noted that,

[...] the organization of the many institutions that govern economic relationships is entirely absent from these [general equilibrium] models. This is particularly striking in the case of firms, which are modeled as a production set. This makes the very existence of firms difficult to justify in the context of general equilibrium models, since all interactions are expected to take place through the price system in these models. (Salanie 2005: 1)

A benefit to these changes in the approach to theory is that these changes have helped stimulated the increase in empirical work we see. The modern theory, in areas as devise as game theory, contract theory, organisational theory, asymmetric information, incentive theory, industrial organisation etc, has lent itself to empirical/experimental testing in a way that the older theory didn't. So theoretical and empirical work has changed together in a way that is mutually reinforcing.

Of course these changes have come with costs as well as benefits.  For example, partial equilibrium models can obscure the importance of the theory of the firm for overall resource allocation, a point which is more easily appreciated in a general equilibrium framework.

Refs.:

• Foss, Nicolai J., Henrik Lando and Steen Thomsen (2000). 'The Theory of the Firm'. In Boudewijn Bouckaert and Gerrit De Geest (eds.), Encyclopedia of Law and Economics (vol. III, 631–58), Cheltenham, UK: Edward Elgar Publishing Ltd.
• Friedman, Milton (1955). "Leon Walras and His Economic System", American Economic Review, 45(5): 900-9.
• Hamermesh, Daniel S. (2013). "Six Decades of Top Economics Publishing: Who and How?", Journal of Economic Literature 51(1): 162-72.
• Salanie, Bernard (2005). The Economics of Contracts: A Primer, 2nd edn., Cambridge MA: The MIT Press.
• Walker, Paul (2016). The Theory of the Firm: An overview of the economic mainstream, London: Routledge.

Limits of general equilibrium

In a recent EconLog piece Emily Skarbek writes,

A recent piece by Raphaële Chappe discusses the uses and limitations of general equilibrium theorizing. The post is a long-read, but Chappe briefly summarizes the point when she writes:

...the theory lacks explanatory relevance, providing instead a language through which one can say both too much and too little. The theory's abundance of riches within its own multiverse is to be contrasted with its complete neglect of some important aspects of real-world markets, such as for example the presence of increasing returns to scale, the role of institutions and their effects (including money), and the place of innovation, all of which are difficult to model within the theory.

This neglect of real-world institutions is very well illustrated by current, mainly partial-equilibrium, approach to the theory of the firm. As I have written in chapter 5 of The Theory of the Firm, the current theoretical approaches to the firm highlight a general issue to do with post-1970 microeconomics; namely, the retreat from the use of general equilibrium (GE) models. I argue,

As early as 1955 Milton Friedman was suggesting that to deal with ‘substantive hypotheses about economic phenomena’ a move away from Walrasian towards Marshallian analysis was required. When reviewing Walras’s contribution to GE, as developed in his Elements of Pure Economics, Friedman argued,

Economics not only requires a framework for organizing our ideas [which Walras provides], it requires also ideas to be organized. We need the right kind of language; we also need something to say. Substantive hypotheses
about economic phenomena of the kind that were the goal of Cournot are an essential ingredient of a fruitful and meaningful economic theory. Walras has little to contribute in this direction; for this we must turn to other economists, notably, of course, to Alfred Marshall.
(Friedman 1955: 908)

By the mid-1970s microeconomic theorists had largely turned away from Walras and back to Marshall, at least in so far as they returned to using partial equilibrium analysis to investigate economic phenomena such as strategic interaction, asymmetric information and economic institutions.

In fact to model economic institutions like the firm it is necessary to violate basic assumptions of GE theory which suggests that as it stands GE cannot deal easily with firms, or other important economic institutions. Bernard Salanié has noted that,

[...] the organization of the many institutions that govern economic relationships is entirely absent from these [GE] models. This is particularly striking in the case of firms, which are modeled as a production set. This makes the very existence of firms difficult to justify in the context of general equilibrium models, since all interactions are expected to take place through the price system in these models.
(Salanié 2005: 1)

All this would suggest that to make GE models a ubiquitous tool of microeconomic analysis – including the analysis of issues to do with non-market organisations such as the firm – developing models which can account for information asymmetries, contractual incompleteness,strategic interaction,the existence of institutions and the like is not so much desirable as essential.

One catalyst for the development of such a new approach to GE is that partial equilibrium models can obscure the importance of the theory of the firm for overall resource allocation, a point which is more easily appreciated in a GE framework.