This paper proposes a concept of the core for games with differential information, using Aumann’s notion of common knowledge. The concept is applied to solve the syndicate problem, for cases in which members have different private information on the uncertain prospects of each syndicate action and the contract (the risk sharing rule and the decision rule) is to be determined before they exchange their information.
[Recent papers which use the framework of temporary equilibrium with rationing to explain unemployment phenomena (sometimes termed "disequilibrium" theory, in which prices do not clear spot markets) are surveyed and evaluated critically. Models which posit fixed prices and then explore the effects of price rigidity are studied. I then consider attempts to explain why prices don't clear markets by considering models in which prices and quantity constraints are simultaneously determined. Many such models are based on perceived demand curves, leading one to consider the viability of unemployment equilibria under various restrictions about correctness or rationality of perceptions. I also consider in detail the role of a medium of exchange and assets in general and show that it is incorrect to link liquidity constraints and quantity rationing.]
It was conjectured by Pigou that an increase in real national income, as reckoned in the prices of either the initial or the terminal period, would always correctly indicate an improvement in national welfare provided the increase referred to the aggregate income of a given group of persons with fixed preferences and a fixed proportional distribution of income among them. We show that if the individual preferences are assumed to be homothetic, and if by a welfare improvement one means respectively a potential improvement (in which losers can be compensated by gainers) or an actual improvement (in which all are gainers), then on either of these respective criteria Pigou's conjecture holds true under these conditions if and only if individual preferences are identical.
[In this paper, Pareto efficiency properties of a non-Walrasian equilibrium for an exchange economy are analyzed. The equilibrium considered is a generalized version of Drèze's equilibrium with price rigidities and rationing.]
In the first part of the paper, a model is proposed which places the Marxian and Sraffian conceptions of a capitalist economy in a general equilibrium framework. A central concern of these writers is that the economy be reproducible; this is incorporated formally into the equilibrium definition. Capitalists maximize profits subject to a capital constraint and workers are paid a subsistence wage. Equilibrium existence theorems are proved. In the second part, the welfare properties of the equilibria are examined-which, in the Marxian tradition, involve the notion of exploitation. It is shown that the possibility of exploitation is necessary and sufficient for all equilibria to sustain positive profits, if a certain technological condition holds. Finally, the notion of a subsistence bundle is dispensed with, and a Marxian determination of workers' consumption is proposed. In addition to placing the formal Marxian model into a general equilibrium context, the specification of production here is more general than the usual Leontief or von Neumann technologies: production sets are assumed to be only convex.
Existing strategies for econometric analysis related to macroeconomics are subject to a number of serious objections, some recently formulated, some old. These objections are summarized in this paper, and it is argued that taken together they make it unlikely that macroeconomic models are in fact over identified, as the existing statistical theory usually assumes. The implications of this conclusion are explored, and an example of econometric work in a non-standard style, taking account of the objections to the standard style, is presented. THE STUDY OF THE BUSINESS cycle, fluctuations in aggregate measures of economic activity and prices over periods from one to ten years or so, constitutes or motivates a large part of what we call macroeconomics. Most economists would agree that there are many macroeconomic variables whose cyclical fluctuations are of interest, and would agree further that fluctuations in these series are interrelated. It would seem to follow almost tautologically that statistical models involving large numbers of macroeconomic variables ought to be the arena within which macroeconomic theories confront reality and thereby each other. Instead, though large-scale statistical macroeconomic models exist and are by some criteria successful, a deep vein of skepticism about the value of these models runs through that part of the economics profession not actively engaged in constructing or using them. It is still rare for empirical research in macroeconomics to be planned and executed within the framework of one of the large models. In this lecture I intend to discuss some aspects of this situation, attempting both to offer some explanations and to suggest some means for improvement. I will argue that the style in which their builders construct claims for a connection between these models and reality-the style in which is achieved for these models-is inappropriate, to the point at which claims for identification in these models cannot be taken seriously. This is a venerable assertion; and there are some good old reasons for believing it;2 but there are also some reasons which have been more recently put forth. After developing the conclusion that the identification claimed for existing large-scale models is incredible, I will discuss what ought to be done in consequence. The line of argument is: large-scale models do perform useful forecasting and policy-analysis functions despite their incredible identification; the restrictions imposed in the usual style of identification are neither essential to constructing a model which can perform these functions nor innocuous; an alternative style of identification is available and practical. Finally we will look at some empirical work based on an alternative style of macroeconometrics. A six-variable dynamic system is estimated without using 1 Research for this paper was supported by NSF Grant Soc-76-02482. Lars Hansen executed the computations. The paper has benefited from comments by many people, especially Thomas J. Sargent
Over two decades ago, Charles Tiebout conjectured that in economies with local public goods, consumers vote with their feet and that this voting creates an approximate market-type equilibrium. He hypothesized that this approximate equilibrium is and, the smaller the moving costs, the closer the equilibrium is to an optimum. This paper provides a formal model of an economy with a local public good and endogenous jurisdiction structures (partitions of the set of agents into jurisdictions) which permits proofs of Tiebout's conjectures. Analogues of classical results pertaining to private-good economies, such as existence of equilibrium and convergence of the core to equilibrium states of the economy, are obtained for the approximate equilibrium and approximate cores. IN HIS SEMINAL PAPER Charles Tiebout [12] argued that the movement of consumers to jurisdictions where their wants are best satisfied, subject to their budget constraints and given (lump sum) taxes within jurisdictions, would lead to near optimal provision of a local public good. In addition, he hypothesized that the larger the economy and the number of jurisdictions and the smaller the moving costs, the nearer the equilibrium would be to an state of the economy. This paper provides proofs of Tiebout's conjectures for local public good economies with endogenous jurisdiction structures (partitions of the set of agents into jurisdictions). An E-core, similar to the Shapley-Shubik weak E-core (in [10]), is defined and it is shown that the E-core is non-empty for all sufficiently large economies. For small E and large economies, points in the E -core have the property that the utilities of consumers are nearly equal to the utilities they would realize at a point in the core of an associated economy with a non-empty core (an economy where agents can be appropriately partitioned into jurisdictions); informally, the E-core shrinks to the core. An E-equilibrium is defined and shown to be in the E -core; therefore, for small E, the E -equilibrium states of the economy are Pareto optimal. In addition, for small E, an s-equilibrium has the properties that: the utilities of consumers are nearly 2 equal to their utilities in a local public equilibrium allocation; and the lump sum taxes paid by most consumers are equal to the Lindahl prices times the quantities consumed of the local public good minus profit shares (the profit shares consumers nearly receive are the per capita profits in local public good
[The purpose of this study is to introduce a measure of inter-income inequality that complements the traditional ones proposed by Gini, Theil, and others. The latter are measures that account for the degree of income inequality within a given population of economic units (called here intra-income inequality ratios) while the former is intended to measure the degree of inequality between income distributions, which is called here economic distance ratio. The generalized mathematical form of this ratio is provided and two particular forms of economic distances ratios are identified. They are presented under both the discrete form, which is distribution-free, for a direct application to observed income distributions, and the parametric form corresponding to a given model of income distribution. Applications are made to the five economic regions of Canada and to white and black family income distributions of the U.S.A.]