**The Relativity Theory of General Economic Equilibrium**

Consider the Second Welfare Theorem: under the Arrow-Debreu system, for every Pareto optimal allocation, there exists an initial endowment of resources such that that allocation is an equilibrium. This is literally the main justification for the benefits of the market: if we reallocate endowments, free exchange can get us to any Pareto optimal point, ergo can get us to any reasonable socially optimal point no matter what social welfare function you happen to hold.

How valid is this justification?

Even if it unique, will we reach it? No: if it is not a stable equilibrium, it is only by dint of luck that our price adjustment process will ever reach it.

## General equilibrium theory - Wikipedia

In the s, Walras showed us that demand and supply, with agents as price takers, can generate supremely useful insights into the economy. Since demand matters, changes in demand in one market will affect other markets as well. If the price of apples rises, demand for pears will rise, as will their price, whose secondary effect should be accounted for in the market for apples.

By the s we have the beginnings of a nice model of individual choice based on constrained preference maximization. Taking prices as given, individual demands have well-defined forms, and excess demand in the economy can be computed by a simple summing up. So we now want to know: is there in fact a price that clears the market?

These equilibrium prices always give Pareto optimal allocations, as had long been known, but there also always exist endowments such that every Pareto optimal allocation is an equilibria. It is a beautiful and important result, and a triumph for the intuition of the invisible hand it its most formal sense. Alas, it is there we reach a dead end. Individual preferences alone do not suffice to tell us what equilibria we are at, nor that any equilibria will be stable, nor that any equilibria will be reached by an economically sensible adjustment process.

To say anything meaningful about aggregate economic outcomes, or about comparative statics after modest shocks, or about how technological changes change price, we need to make assumptions that go beyond individual rationality and profit maximization.

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This is, it seems to me, a shock for the economists of the middle of the century, and still a shock for many today. We learned a great deal about precisely when markets could even in principle achieve the first best, and that education was critical for the work Arrow would later do on health care, innovation, and the environment, which I will discuss in the next two posts.

But it does mean that individual rationality as the sole paradigm of economic analysis is dead: it is mathematically proven that postulates of individual rationality will not allow us to say anything of consequence about economic aggregates or game theoretic outcomes in the frequent scenarios where we do not have a unique equilibria with a well-defined way to get there via learning in games, or a tatonnament process in GE, or something of a similar nature.

Arrow himself , J. Some notes on the literature: For those interested in the theoretical development of general equilibrium, I recommend General Equilibrium Analysis by Roy Weintraub, a reformed theorist who now works in the history of thought. Wade Hands has a nice review of the neoclassical synthesis and the ways in which Keynesianism and GE analysis were interrelated.

On the battle for McKenzie to be credited alongside Arrow and Debreu, and the potentially scandalous way Debreu may have secretly been responsible for the Arrow and Debreu paper being published first, see the fine book Finding Equilibrium by Weintraub and Duppe; both Debreu and McKenzie have particularly wild histories.

I would be interested to know if you think computable agent-based models are the way forward. As in:. I have enjoyed reading your last two posts on Arrow. You are clearly an authority on many subjects in economics, and I believe that the field can learn a lot from your deep knowledge of economic history. Specifically, how can he be considered a titan in economics when his model of ge does not encompass money? Secondly, and which you mention much more in your first article on Arrow, is considering Arrow as one of the greatest economists because of his dedication to mathematical economics.

But this is assuming that mathematizing economics is a beneficial.

And while I believe that math plays an important role in economics, I believe the way economists have used math is generally destructive manner by insulating the field from other social sciences. Thus, when both of these arguments are combined, the limits of general equilibrium and the overuse of mathematics in economics, I am lead to the conclusion that others have also arrived at: these developments HURT policymakers and economists from accurately foreseeing the financial crisis.

By developing highly mathematized models that demonstrated that the economy was at equilibrium, it created the conditions where economic theory was detached from the workings of the actual economy. While I do believe Arrow has contributed to the field of economics, as you have clearly stated, it does not necessary mean he has influenced the field in a positive light.

I enjoy reading your articles, and will follow for many more, as you offer a lot to learn from. Arrows contribution to economics, and its impacts on the field, however, remain questionable. I think critically about the ideas and concepts Arrow suggests. And when his ideas are then applied, perhaps foolishly by other economists, central bankers and politicians— it has done more damage than good to the real economy. If you want to contend that complacency and myopia in parts of Economics, e.

So you need a better language to pin down what you think policymakers did wrong. Arrow was definitely great, in this sense. I think he also gets a great deal of respect from heterodox economists who would not go along with him. The idea here is not the claim that unregulated markets will lead to optimality, but that government policy should try to construct markets, including markets for derivatives, to be more like the model.

I do not agree with the depiction of classical economics here, but put that aside. Sometimes, they seem to accept that multiple equilibria can be determinate, as long as they are not discrete. The claim seems to be that multiple equilibria do not lie along a continuum in some space of endogenous variables. Article Navigation. Close mobile search navigation Article Navigation.

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### 1st Edition

Add to Cart. More about this book. Chapter 1 [PDF]. Polyrakis, Mathematical Reviews Clippings. This will be an excellent text for advanced graduate students in economic theory, an introduction for mathematics students with an interest in applications of differential topology, and a must-have reference for researchers in general equilibrium theory.

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Spear, Carnegie Mellon University.