This is an interesting question.
There is a tradition of general equilibrium models (even if the phrase 'general equilibrium' needs to be specified) that assumes prices as exogenously given.
They are known as disequilibrium models or non-Walrasian equilibrium models.
The term disequilibrium models is probably inappropriate, as actually they are true equilibrium models, taking into considerations all markets, even though they define a different concept of equilibrium.
This is not the usual notion of the so-called Walrasian equilibrium, which defines equilibrium as a situation in which markets clear, that is (Walrasian) demand is equal to supply in each market. But it defines a notion of equilibrium which is compatible with excess demand different from zero in the markets, that is unbalances between demands and supplies.
These models, indeed, are in the wake of general equilibrium models, in that they define and analyze equilibrium positions of the system, rather than relying on an analysis of markets outside equilibrium. And, also, they are grounded on rigorous microeconomic foundations.
The point is that they define a concept of equilibrium different from the usual Walrasian concept, so these equilibria are called non-Walrasian equilibria.
In the traditional Walrasian paradigm, there is some (unspecified) mechanism (the so-called tâtonnement process), by which a hypothetical, fictional, 'auctioneer' changes the prices until a Walrasian equilibrium vector prices is reached. This equilibrium prices vector is characterized by the equality of aggregate demand and supply in all markets.
At this point, trade takes place, transactions are equal to demand and supplies and no quantity constraint is perceived by any agent (they perceive they can sell and buy what they want).
On the contrary, in non-Walrasian equilibrium models, this process of tâtonnement on prices is, by assumption, absent.
The main assumptions of these models are:
- Prices are fixed, exogenously given, in each market;
- no tâtonnement on prices exists, so that trades are allowed out of (Walrasian) equilibrium, that is in situations where demands and supplies are not equal, at those fixed prices;
- agents now perceive quantity constraints on their demand/supply: in non-market clearing models we must distinguish between demand/supply and actual transactions. As demand/supplies in non-market clearing conditions cannot be all satisfied, it is necessary to define a rationing scheme (for example, queueing);
- now agents perceive quantity constraints (rationing), so that they will take into account in their demands/supplies also these quantitative signals (the actual quantities they can buy or sell).
Therefore, these models use different functions of demand and supply with respect to the usual demand and supply functions. These latter depend only on prices and on initial endowments, whereas in non-Walrasian fixed prices models agents will react also to quantity signals, that is their demands/supplies depend also on the actual transaction they realize.
This is a new concept of demand, called effective demand, as opposed to the usual, Walrasian demand/supply, called sometimes also notional demand.
On this basis, a new concept of equilibrium is defined, in which the actions of rational agents taking into account quantity signals are made compatible, even if excess Walrasian demand are different from zero: these equilibria (which of course are formally defined in these models) are called non-Walrasian equilibria.
There is a tradition of literature on non-Walrasian equilibria, both from a microeconomic and a macroeconomic point of view.
As for microeconomics, there are economists as Benassy (1975) and Drèze (1975) , as for macroeconomics there is a Keynesian tradition, beginning with Patinkin (1956) and Clower (1965), and continued by authors as Malinvaud (1977), Barro and Grossmann (1971), and also Benassy (1977).
From a macroeconomic point of view, these 'disequilibrium' or 'non-Walrasian ' models constitute a reappraisal of Keynesian theory, and of the concept of Keynesian effective demand.
In this respect, this non-Walrasian literature intended also to be a possible microeconomic foundation of Keynesian macroeconomics, filling the gap between macroeconomic and microeconomic theory and providing microeconomic foundations to Keynesian macroeconomics with unemployment configurations.
Of course, the theoretical weakness of these theories is the fixed price assumption. This literature did not receive general acceptance, and it is criticized because it fails to explain why prices are so sticky to justify a permanent situation of unemployment. Some authors tried to go beyond fixed prices assumption, as Frank Hahn by his conjectural equilibria.
Some authors, as Benassy (2002), continued this tradition of analysis of non-clearing markets, abandoning the assumption of perfect competition, and assuming imperfect competition and the presence of price makers in the economy.
Or, other authors tried to overcome the static nature of these models, introducing dynamic aspects that could explain the intertemporal dynamics of prices.
A recent discussion of this subject can be found in Böhm, (2017), chap. 6-7.
Barro R. J., & Grossman, H. I., (1971), A General Disequilibrium Model of Income and Unemployment, American Economic Review, mar: 82-93.
Benassy, J. P., Disequilibrium Exchange in Barter and Monetary Theory,(1975) Economic Inquiry, jun: 503:523.
Benassy, J. P., The quantity Signals and the Foundations of Effective Demand Theory, (1977), Scandinavian Journal of Economics, 79: 147-168.
Benassy, J.P., The Macroeconomics of Imperfect Competition and Nonclearing Markets-A Dynamic General Equilibrium Approach, 2002, MIT Press.
Böhm, Macroeconomic Theory (2017), Springer.
Clower, R. W., The Keynesian Counterrevolution: A Theoretical Appraisal, (1965) , in The Theory of Interest Rates, ed. By F. H. Hahn & Brechling, Lonon, macMillan.
Drèze, J. H., Existence of Exchange Equilibrium under Price Rigidity, (1975), International Economic Review 16, 301-320.
Hahn, F., On Non-Walrasian Equilibria, (1978), Review of Economic Studies, feb: 1-17.
Malinvaud , E., The Theory of Unemployment Reconsidered , (1977), Blackwell Publishers, Oxford.
Patinkin, D., Money, Interest and Prices, (1965) Harper & Row, New York.