The thing that the standard GE model tries to model is the price system. As has been pointed out by Demsetz (1982, 1988 and 1995) the fundamental preoccupation of economists, right up until the 1930s and beyond in many cases, was with the price system. The interest in the price system, culminating in the "perfect competition" model, has its intellectual origins in the eighteenth-century debate between free traders and mercantilists. This debate was, at its simplest, about the proper scope of government in an economy, and the model it gave rise to reflects this. The central question of the debate was, Is central planning necessary to avoid the problems of a chaotic economic system? Adam Smith famously answered no.
For Smith, markets are one very prominent mechanism for solving the problems of coordination and motivation that arise with interdependencies of specialisation and the division of labour. Market institutions leave individuals free to pursue self-interested behaviour, but guide their choices by the prices they pay and receive. The 200 hundred years following Smith amounted to a closer examination of the conditions necessary for the price system alone to be able to avoid chaos.
The formal model that arose from this examination is one which abstracts completely from any form of centralised control in the economy. This is an abstraction Smith myself would have argued was going too far. Smith knew of the importance of institutions to the proper functioning of the market economy. But the point of the modelling was to remove those very institutions so that the price system is the only mechanism available to coordinate and control the economy. It is a model delineated by "perfect decentralisation", to use Demsetz's term. Authority, be it in the form of a government or a firm or a household, plays no role in coordinating resources. The only parameters guiding decision making are those given within the model - tastes and technologies - and those determined impersonally on markets -prices. All parameters are outside the control of any of the economic agents and this effectively deprives all forms of authority a role in allocation. This includes, of course, the government, the firm and the household. We are left with a world only controlled by the price system.
The amazing thing is that it can be shown that chaos does not result in such a system. This is what the standard results on the existence, uniqueness and stability of equilibrium in the general equilibrium model tell us. See, for example, Debreu (1959) if you must.
- Debreu, Gerard (1959). Theory of Value, New York: Wiley.
- Demsetz, Harold (1982). Economic, Legal, and Political Dimensions of Competition, Amsterdam: North-Holland Publishing Company.
- Demsetz, Harold (1988). 'The Theory of the Firm Revisited', Journal of Law, Economics, and Organization, 4(1) Spring: 141-61.
- Demsetz, Harold (1995). The Economics of the Business Firm: Seven Critical Commentaries, Cambridge: Cambridge University Press.