Decentralization in Infinite Horizon Economies

The following sections are included:

• Contents
• Preface
• Foreword
• Acknowledgments

The paper summarizes some issues involved in developing a theory of decentralized resource allocation mechanism in infinite horizon economies. Even in a classical environment, a competitive mechanism may lead to an inefficient or non-optimal allocation for an infinite horizon economy. It remains, however, to explore whether the usual price-quantity messages can be supplemented to design decentralized mechanisms generating optimal outcomes.

Problems of achieving an efficient or optimal allocation of resources through a system of decentralized decision-making when the planning horizon is unbounded and the number of agents is infinite have been repeatedly raised, but have not been explored in a formal manner. The objective of this paper is to suggest some points of departure for a systematic investigation of such questions. The main analytical results indicate the impossibility of attaining optimality through intertemporally decentralized mechanisms.

The paper considers a multisector model of intertemporal allocation with a primary factor of production and the overtaking criterion of optimality. The optimal program is characterized in terms of (i) period-by-period conditions on intertemporal profit and utility maximization relative to a system of competitive prices and (ii) non-positivity of appropriately computed values of differences of stocks from the golden rule stock: The last condition replaces the usual transversality condition of Malinvaud and throws new light on the possibility of dencentralization in an infinite-horizon economy.

The paper studies the problem of characterizing the optimality of competitive programs in terms of “decentralizable” conditions. We show that, when future utilities are discounted, and the optimal stationary stock is proportionately expansible, then optimality of competitive programs can be characterized by the condition that the scalar product of the difference of prices and quantities, between those of the given competitive program and those of the optimal stationary program, be non-positive period by period.

The paper presents the main results on intertemporal optimality with discounting in a closed linear model of production, including the price characterization of optimal programs, the existence of a steady-state optimal program, and a turnpike property of optimal programs from arbitrary initial stocks. Some of these results are used to provide a characterization of the optimality of competitive programs in terms of a “decentralizable” condition.

A condition is provided to replace the transversality condition in characterizing the optimality of competitive processes. This extends the work of W. Brock, L. Hurwicz, and M. Majumdar (“On Characterizing Optimality of Competitive Programs in Terms of Decentralizable Conditions” and “Optimal lntertemporal Allocation Mechanisms and Decentralization of Decisions,” Cornell University Working Paper Nos. 333 and 369 (1985)) on providing an informationally decentralizable condition for characterizing optimality in stochastic infinite-horizon models without discounting.

The following sections are included:

• INTRODUCTION
• THE MODEL
• FEASIBLE PROGRAMS
• OPTIMAL PROGRAMS
• FINITE HORIZON PROGRAMS
• A CRITICAL STOCK
• RESULTS
• REFERENCES

A necessary condition for realization by a decentralized finite-dimensional mechanism is proved. The concepts of the realization of a time sequence of allocations by a decentralized temporal process and by the particular more realistic class of decentralized evolutionary temporal processes are defined. The above condition shows that the optimal allocation in a simple model for intertemporal production and consumption can be realized by a decentralized temporal process but not by a decentralized evolutionary process which uses either a finite number of verification conditions or a finite-dimensional message space.

We consider a stationary, inlinite horizon aggregative model with one consumer and one producer living in each period. A decentralized intertemporal mechanism, satisfying the following “evolutionary” property, is constructed: if the current period's producer and consumer verify their equilibrium conditions, then the allocation is actually executed, without further verification by future agents. The mechanism is based on the idea of continual planning revision. It is shown that the outcome is an intertemporally efficient allocation which maximizes the long run average of one period utilities from consumption.

Here I sketch some of the proofs left out in the published version, add a few comments and report on some new results. First, let me start with some details.

The following sections are included:

• About the Book and Editor
• Contributors