Joseph M. Ostroy

Flexibility and Uncertainty

The preserving of flexibility when faced with uncertainty is a neglected aspect of behaviour under risk. Yet it is an important factor in decisions to hold liquid assets or delay irreversible investment. This paper formalizes the notion of flexibility in a sequential decision context, and relates its value to the amount of information an agent expects to receive. A rudimentary money demand model is developed embodying these ideas, and the history of flexibility as an economic concept is traced.

The Transactions Role of Money

Publisher Summary The transaction role of money is one of the most palpable of economic phenomena and offers one of the first challenges for the theory of exchange. A useful analogy can be made between the role of money as a record-keeping device and the theory of signaling. The chapter discusses that the theory of exchange was developed as a response to the challenges of price determination and allocation of resources. The frictions required for monetary exchange—such as differential costs of spot and forward transactions and the strategic issues of incomplete information and incentive compatibility—are recent developments. It explains the slow growth of the transaction role of money as a branch of the theory of exchange. The transaction role of money challenges the implicit logistical and informational assumptions of the theory of exchange. The sequential nature of trade makes informational demands that go beyond the knowledge of prices that suffices in the traditional theory of exchange. The chapter also examines the rationale behind the transaction role of money in a model exhibiting this dichotomy. Exploring the properties of models in which budget enforcement problems are always a binding constraint on behavior helps illuminate the understanding of macroeconomics.

The nonatomic assignment model

SummaryWe formulate a model with a continuum of individuals to be assigned to a continuum of different positions which is an extension of the finite housing market version due to Shapley and Shubik. We show that optimal solutions to such a model exist and have properties similar to those established for finite models, namely, an equivalence among the following: (i) optimal solutions to the linear programming problem (and its dual) associated with the assignment model; (ii) the core of the associated market game; (iii) the Walrasian equilibria of the associated market economy.

Ascending price Vickrey auctions

Abstract We show that an ascending price auction for multiple units of a homogeneous object proposed by Ausubel (i) raises prices for packages until they reach those nonlinear and non-anonymous market clearing prices at which bidders get their marginal products and (ii) the auction is a primal–dual algorithm applied to an appropriate linear programming formulation in which the dual solution yields those same market clearing prices. We emphasize the similarities with efficient incentive compatible ascending price auctions to implement Vickrey payments when there is a single object or when objects are heterogeneous but each buyer does not desire more than one unit. A potential benefit of these common threads is that it helps to establish the principles upon which Vickrey payments may be implemented through decentralized, incentive compatible procedures.

Nonatomic Economies and the Boundaries of Perfect Competition

The distinction between nonatomicity and thick markets as the source of perfect competition is examined. The authors construct a model of an imperfectly competitive economy with a nonatomic continuum of traders and a continuum of differentiated commodities for which Walrasian equilibria exist. The failure of perfect competition is identified in two ways: individuals can affect prices and the core is strictly larger than the set of Walrasian allocations. By contrast, it is shown that, when markets are physically or economically thick (or both), then individuals cannot typically affect prices and the core always coincides with the set of Walrasian allocations. Copyright 1994 by The Econometric Society.

Vickrey-Clarke-Groves mechanisms and perfect competition

Abstract We present a game theoretic-mechanism characterization of perfect competition: we prove the perfectly competitive mechanism is the only Pareto optimal, individually rational, dominant strategy allocation mechanism. Thus, perfect competition is uniquely capable of efficiently and non-coercively solving the incentive/bargaining problem when there is incomplete information, i.e., when each individual knows his own tastes and production possibilities better than anyone else. We also show one can interpret any dominant strategy, demand-revealing mechanism as “working” because it mimics the reward scheme that characterizes the perfectly competitive market, namely, the marginal product reward scheme.

A REFORMULATION OF THE MARGINAL PRODUCTIVITY THEORY OF DISTRIBUTION

Reformulating marginal productivity theory by replacing productivity with respect to commodities with productivity with respect to persons and then defining perfectly competitive equilibrium as an allocation at which each person receives the marginal product of his/her contribution called a no-surplus allocation there emerges a competitive theory of price determination. Characterizations of no-surplus allocations are given in models with a nonatomic continuum of agents and an infinite-dimensional commodity space. Comparisons between the no-surplus and Walrasian equilibrium definitions of competitive equilibrium are made and some sufficient conditions are obtained for the existence of a no-surplus allocation.

On the existence of walrasian equilibrium in large-square economies

Abstract An existence theorem for Walrasian equilibrium is demonstrated for an economy with a continuum of consumers and an infinite-dimensional commodity space, such as l 1 or c 0 , having an ‘order-compatible’ basis.

Thick and Thin Market Nonatomic Exchange Economies

Perfect competition — that situation in which no individual has the ability to influence prices — has traditionally been regarded as requiring large number of traders. Aumann [4] gave mathematical precision to a model with large numbers by regarding the set of traders as a nonatomic measure space. He showed that such a model passed a test of competitiveness whose origins go back to Edgeworth [16]: the game-theoretic solution concept of the core coincides with the market-demand-equals-supply notion of Walrasian, price-taking equilibrium. Related results are contained in [12] and [22].

Vickrey-Clarke-Groves mechanisms in continuum economies: Characterization and existence

Abstract The equivalence in the finite agent model between the families of efficient dominant strategy and Vickrey-Clarke-Groves mechanisms is extended to continuum economies. The concept of an individuals marginal product is used to link the two families of mechanisms when agents are non-atomic. Unlike the finite agent model, feasible and efficient dominant strategy mechanisms exist in the continuum, but these mechanisms do not guarantee individual rationality. For individual rationality to hold, the environment must also satisfy full-appropriation : each individual receives a payoff exactly equal to his/her marginal product. Full-appropriation is shown to be equivalent to the condition that each individual fully internalizes any external effects he/she creates. Environments and examples are given that exhibit or fail to exhibit full-appropriation.