Where Do Prices Come From In Marginalist Economics?

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Robert Vienneau
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Where do prices come from in mainstream economics? As far as I know, some hard questions were raised half a century ago. They still have not been answered, I gather.

Consider competitive markets, as defined in marginalist economics for most of the twentieth century. This implies that agents in the market take prices as given.

From Steve Keen, I know that if only a countable infinity of consumers and firms exist, the agents are systematically mistaken. Despite their beliefs, they are not atomic, and their actions in varying quantities bought or sold affect prices. For agents not to be systematically mistaken, an uncountable infinity of consumers and firms must exist.

I have noted Emmanuelle Benicourt making similar points before.

Classical political economy provides another concept of competitive markets. This concept is that no barriers to entry or exit exist. This concept has been taken into mainstream economics under the rubric of contestable markets.

If all agents take prices as given, who makes prices?

"How can equilibrium be established? ... Do individuals speculate on the equilibrium process? If they do, can the disequilibrium be regarded as, in some sense, a higher-order market process? Since no one has market power, no one sets prices; yet they are set and changed. There are no good answers to these questions." -- Kenneth Arrow (1987)

Franklin Fisher did some work here which he agrees is not a fully satisfactory answer. In his investigation of disequilibrium, convergence to an equilibria requires the ad-hoc assumption of 'No favourable suprise'. Furthermore, the equilibrium that is found will generally not correspond to the initial data. The disequilibrium process changes the data, for example, the initial distribution of endowments.

Suppose one wants to model production. Many economists turned away from long run theory, towards analyzing intertemporal equilibrium paths. Even though I have done work in signal processing, I do not not feel comfortable with optimal control theory.

Some general objections can be raised to this whole approach. For example, initial endowments are among the givens. If some were previously produced, a failure to fulfill expectations is possible. But an equilibrium position is one in which all expectations are fulfilled in the future.

As I understand it, markets always clear at all moments in time along an equilibrium path. For given initial conditions, typically an uncountable infinity of such paths exist. Some of these paths result in the economy eventually reaching a point in which capital goods needed to keep the economy going are just not produced. Other paths approach a path for steady-state growth, from which they will eventually diverge. Frank Hahn argued that, given multiple capital goods, an infinite number of steady-state growth paths exist. How one of these paths is picked out is the 'Hahn problem'. Some paths neither lead to the economy collapsing or a steady state. Instead, they lead to cycles.

I am not clear what is typically assumed about expectations. I guess myopic expectations are needed, in some sense, for the existence of equilibrium paths that end up with the economy crashing.

Reswitching appears in this literature. Michael Bruno has a paper in Shell (1967) that has equilibrium paths just skipping over a reswitching regime. Rosser identifies this possibility with a cusp catastrophe. Maybe an issue arises here with how an equilibrium path can approach a steady state. Is this what Hahn refers to in the closing paragraphs of Hahn (1982).

I guess economists typically assume that the economy will not follow a path in which the economy cannot continue to be sustained. And initial prices are such that one unique path is picked out. Typically this path converges to a steady state growth path which has the stability of a saddle poing.

My references are not recent. Maybe I want to read something by William Brock. As far as I know, marginalist economic theory still has these problems. I guess mainstream economists just assume transversality conditions, with no theory of how equilibrium is reached or why the equilibrium path that is found does not lead to collapse.

• Kenneth J. Arrow. 1987. Economic theory and the hypothesis of rationality, The New Pagrave: A Dictionary of Economics.
• Robert Aumann. 1964. Markets with a continuum of traders. Econometrica, 32 (1-2): 39-50.
• Emmanuelle Benicourt. 2016. Is the core e-Book a possible solution to our problems?, Real-World Economics Review, 75: 135-142
• Robert Dorfman, Paul Samuelson, and Robert Solow. 1958. Linear Programming and Economic Analysis.
• Franklin M. Fisher. 1983. Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press.
• Harvey Gram and G. C. Harcourt. 2017. Joan Robinson and MIT, History of Political Economy 49(3): 437-450.
• Frank Hahn. 1982. The neo-Ricardians, Cambridge Journal of Economics 6(4): 353-374.
• Frank Hahn. 1987. 'Hahn problem', The New Pagrave: A Dictionary of Economics.
• J. Barkley Rosser Jr. 1983. Reswitching as a cusp catastrophe, Journal of Economic Theory 31(1): 182 - 193.
• Karl Shell (ed.). 1967. Essays on the Theory of Economic Growth, MIT Press.