28.2.17

COMPETITIVE MARKETS ALLOCATE RESOURCES EFFICIENTLY.

This tribute to the recently departed Kenneth Arrow, at A Fine Theorem, clarifies how restrictive the sufficient conditions for emergent Pareto efficiency are.  I'll even cut the author some slack for believing in the Fatal Conceit.
My read of the literature on [general equilibrium] following Arrow is as follows. First, the theory of general equilibrium is an incredible proof that markets can, in theory and in certain cases, work as efficiently as an all-powerful planner. That said, the three other hopes of general equilibrium theory since the days of Walras are, in fact, disproven by the work of Arrow and its followers. Market forces will not necessarily lead us toward these socially optimal equilibrium prices. Walrasian demand does not have empirical content derived from basic ordinal utility maximization. We cannot rigorously perform comparative statics on general equilibrium economic statistics without assumptions that go beyond simple utility maximization. From my read of Walras and the early general equilibrium theorists, all three of those results would be a real shock.
Repeat with me: there is no such thing as an all-powerful planner.  That noted: existence of competitive equilibrium follows from a narrow set of sufficient conditions.  Uniqueness and stability of that equilibrium: harder still.  On the flip side, the absence of the sufficient conditions does not lead inexorably to a set of circumstances where Someone In Authority (not necessarily an all-powerful planner) can find a Pareto improvement.  It's even hard in the presence of the sufficient conditions.
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? Call x* the allocation that maximizes some social welfare function. Let e* be an initial endowment for which x* is an equilibrium outcome – such an endowment must exist via Arrow-Debreu’s proof. Does endowing agents with e* guarantee we reach that social welfare maximum? No: x* may not be unique. 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.
There are some subtleties involving separating hyperplanes that the reader must understand, before giving up on the case for rearranging endowments.  But "main justification for the benefits of the market?"  It's probably harder than that: has anyone come up with a set of sufficient conditions under which Partially Informed Wise Experts achieve an allocation of resources that is Pareto-superior to an allocation of resources that Partially Informed participants in a distributed network reach.  Impound nonconvexities, including externalities and club goods, in ceteris paribus and tell me what you come up with.

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