, Volume 12, Issue 3, pp 30-44

The millions of equations debate: Seventy years after Barone

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Conclusion

The general study of allocation mechanisms began with Barone's work, which established the theoretical feasibility of an alternative allocation mechanism. There were a number of aspects of the problem that Barone did not explicitly take into account, and it seemed that the central planner would have to solve millions of equations for feasibility and optimality of the allocation. Lange and Taylor were among the first to claim that if the parametric role of prices is kept, the problem of millions of equations would not arise. Socially desirable outcomes could be achieved in a decentralized manner, even without private property. The modern research has established rigorously the conditions under which this can be done.

The 70-year-old debate on the feasibility of socialist planning identified at least three problem areas: the lack of an acceptable, all embracing and complete social criterion function, the problem of incentives, and the magnitude of the informational load. This review attempts to show that these issues continue to dominate modern research in the theory of allocation mechanisms.

The first named author's research was financed by a grant (no. 410-80-0552) from the Social Sciences and Humanities Research Council of Canada. However the authors alone are responsible for the views expressed here.