Stationary measures for some Markov chain models in ecology and economics

Summary. Let continuous, exists in for x in . Let be an i.i.d. sequence from F and X₀ be a nonnegative random variable independent of . Let be the Markov chain generated by the iteration of random maps by . Such Markov chains arise in population ecology and growth models in economics. This paper studies the existence of nondegenerate stationary measures for {X_n}. A set of necessary conditions and two sets of sufficient conditions are provided. There are some convergence results also. The present paper is a generalization of the work on random logistics maps by Athreya and Dai (2000).Received: 20 March 2002, Revised: 4 December 2002, JEL Classification Numbers: C22, D9.The author wishes to thank Professor Mukul Majumdar and the referees for several useful suggestions.     

Voting in assemblies of shareholders and incomplete markets

Summary. An economy with two dates is considered, one state at the first date and a finite number of states at the last date. Shareholders determine production plans by voting - one share, one vote - and at -majority stable stock market equilibria, alternative production plans are supported by at most percent of the shareholders. It is shown that a -majority stable stock market equilibrium exists if where S is the number of states at the last date and J is the number of firms. Moreover, an example shows that -majority stable stock market equilibria need not exist for smaller s.Received: 23 December 2002, Revised: 14 June 2004, JEL Classification Numbers: D21, D52, D71, G39. Correspondence to: Hervé CrésThe authors are grateful to an anonymous referee for helpful comments and suggestions. Financial support from the Danish Research Councils and hospitality of HEC is gratefully acknowledged by Mich Tvede and support from Fondation HEC is gratefully acknowledged by Hervé Crés.     

Equilibria and Pareto optima of markets with adverse selection

Summary This paper examines the efficiency properties of competitive equilibrium in an economy with adverse selection. The agents (firms and households) in this economy exchange contracts, which specify all the relevant aspects of their interaction. Markets are assumed to be complete, in the sense that all possible contracts can, in principle, be traded. Since prices are specified as part of the contract, they cannot be used as free parameters to equate supply and demand in the market for the contract. Instead, equilibrium is achieved by adjusting the probability of trade. If the contract space is sufficiently rich, it can be shown that rationing will not be observed in equilibrium. A further refinement of equilibrium is proposed, restricting agents' beliefs about contracts that are not traded in equilibrium. Incentive-efficient and constrained incentive-efficient allocations are defined to be solutions to appropriately specified mechanism design problems. Constrained incentive efficiency is an artificial construction, obtained by adding the constraint that all contracts yield the same rate of return to firms. Using this notion, analogues of the fundamental theorems of welfare economics can be proved: all refined equilibria are constrained incentive-efficient and all constrained incentive-efficient allocations satisfying some additional conditions can be decentralized as refined equilibria. A constrained incentive-efficient equilibrium is typically not incentive-efficient, however. The source of the inefficiency is the equilibrium condition that forces all firms to earn the same rate of return on each contract.Notation ={ ₁,..., _k } set of outcomes - : ₊ generic contract or lottery - A = () ; - A_o A{, where denotes the null contract or no trade - S={1,...,¦S¦} set of seller types - L(s) number of type-s sellers - M number of buyers - u: × S seller's utility function, which can be extended toA× S by puttingu(, s) ; - v. × S buyer's utility function, which can be extended toA × S by puttingv(, s) ; - f:A ₀ ×S ₊ allocation of sellers - g:A ₀ ×S ₊ allocation of buyers - A ₊ sellers' trading function - :A ×S ₊ buyers' trading function This paper has had a long gestation period, during which I have been influenced by helpful conversations with many persons, by their work, or both. Among those who deserve special mention are Martin Hellwig, Roger Myerson, Edward Prescott, Robert Townsend and Yves Younés. Earlier versions were presented to the NBER/CEME Conference on Decentralization at the University of Toronto and the NBER Conference on General Equilibrium at Brown University. I would like to thank John Geanakoplos, Walter Heller, Andreu Mas Colell, Michael Peters, Michel Poitevin, Lloyd Shapley, John Wooders, Nicholas Yannelis and an anonymous referee for their helpful comments and especially Robert Rosenthal for his careful reading of two drafts. The financial support of the National Science Foundation under Grant No. 912202 is gratefully acknowledged.     

An axiomatic approach to \boldsymbol{\varepsilon}-contamination

Summary.  Suppose that an economic agent is 100% certain that uncertainty she faces is characterized by a particular probability measure, but that she has a fear that, with 100% chance, her conviction is completely wrong and she is left perfectly ignorant about the true measure in the present as well as in the future. This situation is often called -contamination of confidence. The purpose of this paper is to provide a simple set of behavioral axioms under which the decision-makers preference is represented by the Choquet expected utility with the -contamination of confidence.Received: 25 November 2002, Revised: 15 November 2004, JEL Classification Numbers:   D81. Correspondence to: Hiroyuki OzakiWe are grateful to an anonymous referee. The referees comments greatly improved the exposition of the paper. The work reported here is partially supported by a grant from the Economic and Social Research Insitute, the Cabinet Office, the Government of Japan.     

The nature of the steady state in models of optimal growth under uncertainty

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is affected by a multiplicative shock taking one of two values with positive probabilities p and 1-p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever . More delicate is the case . Singularity with respect to Lebesgue measure also appears for values such that . For and Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs .Received: 9 April 2002, Revised: 29 October 2002, JEL Classification Numbers: C61, O41.Correspondence to: Tapan MitraThis research was partially supported by CNR (Italy) under the "Short-term mobility" program and by M.U.R.S.T. (Italy) National Group on "Nonlinear Dynamics and Stochastic Models in Economics and Finance" . We are indebted to Rabi Bhattacharya for providing us with the reference to Solomyak's (1995) paper. The present version has benefitted from comments by Mukul Majumdar and two anonymous referees.     

The extent of the market and optimal specialization

Summary. In this paper I examine how the socially optimal allocation, and specialization in particular, depends on the extent of the market. I interpret the societys ability to keep transaction records as the extent of the market and measure it by a probability with which the society can update agents past transactions into the public record. The society uses this record to detect potential defections from the optimal allocation and to punish the defectors with autarky. I show that when is small, increasing increases optimal specialization. However, when is close to 1, increasing further has no effect on the optimal allocation. I also show that optimal specialization is gradual over time when there is cost to reduce specialization. Even for small , the process converges to the unconstrained optimum that would occur under .JEL Classification Numbers: D60, C78.An earlier version of this paper was presented at the Society for Economic Dynamics meetings in Stockholm (2001). I thank a referee and the editor for useful comments and suggestions. For financial support, I gratefully acknowledge the Social Sciences and Humanities Research Council of Canada, and the Bank of Canada Fellowship. The opinion expressed here is my own and does not reflect the view of the Bank of Canada.     

The “Dorfman Steiner” rule

Conclusion When this research was started, it was guessed that the Dorfman-Steiner rule would lose its relevance in an intertemporal setting. This belief has turned out to be false: along the optimal paths ofp (t) ands (t), and must be equal. The only difference with the Dorfman-Steiner result is that they will be different from unity.The author is chargé de cours at the Faculté Universitaire Catholique de Mons (Belgium). He has greatyl benefited from comments by M. Beuthe and J. J. Lambin.     

From “tax state” to “debt state”

The paper is motivated by Joseph A. Schumpeter's The Crisis of the Tax State. It inquires whether the buildup of government debt in peacetimeprosperity is a threat to the stability, existence or creation of viable tax states. The paper begins by setting out Schumpeter's conception of the tax state and the nature of recent political-economic events which have reinvigorated the concept. Next the paper sets out some simple debt dynamics and sketches a debt-induced business cycle arising from heavy reliance on debt finance in peacetimeprosperity. Finally, the paper assesses threats to the tax state in light of recent work on path dependence and positive feedback. An attempt is made to throw some light on whether the plethora of new, and often small, states spawned by the demise of communism can be viable tax states.Essay on Government, the Tax State and Economic Dynamics submitted to the Third Schumpeter Prize Competition.     

Strategy-proof and individually rational social choice functions for public good economies

Summary We consider the problem of choosing an allocation in an economy in which there are one private good and one public good. Our purpose is to identify the class of procedures of choosing an allocation which satisfy strategy-proofness, individual rationality, no exploitation and non-bossiness. Any such procedure is a scheme of semi-convex cost sharing determined by the minimum demand principle.I wish to thank Professors Salvador Barbera, Matthew Jackson, Herve Moulin and William Thomson for their helpful suggestions and two anonymous referees for their detailed comments. Conversations with Professors Hideo Konishi, Shinji Oseto Ken-ichi Shimomura and Stephen Ching were helpful. This work is supported by the Japan Economic Research Foundation and Research Grants PB89-0294 and PB89-0075 from the Direcion General de Investigacion Cientifica y Tecnica, Spanish Ministry of Education.     

Der Weg zur Konvertibilität

Ohne ZusammenfassungVortrag, gehalten am 26. Mai 1955 in der Nationalökonomischen Gesellschaft in Wien.     

Continuity properties of the private core

Let be a sequence of differential information economies, converging to a limit differential information economy (written as ). Denote by the set of all ε-private core allocations, ε ≥ 0 (for ε=0 we get the private core of Yannelis (1991), denoted by ). Under appropriate conditions, we prove the following stability results

First-order risk aversion and non-differentiability

Summary First-order risk aversion happens when the risk premium a decision maker is willing to pay to avoid the lottery , is proportional, for smallt, tot. Equivalently, 0$$ " align="middle" border="0"> . We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).We are grateful to the Social Sciences and Humanities Research Council of Canada for financial support and to Kim Border, Larry Epstein, Mark Machina and Joe Ostroy for helpful discussions and suggestions.     

Finance,investment and innovation: A theoretical and empirical comparative analysis

The paper compares the relative efficiency of country models in the relationship between finance and investments. Results, confirmed under three different panel data estimates (Arellano-Bond GMM method, random and fixed effect estimates) suggest that: i) the UK thick market reduces informational asymmetries for large firms and for those firms providing good signals to shareholders; ii) the Japanese vertical (between firms and banks) integration and horizontal (among firms) integration almost eliminates financial constraints (the horizontal integration effect) and equates agency costs across firms (the vertical integration effect). These results are consistent with the short-termist hypothesis which assumes that the Japanese economic system can process information more efficiently reducing managerial myopic behaviour and thereby determining positive effects on long term growth.     

Alternative Modelle und Hypothesen der Konsum- und Sparentscheidung(1)

Summary For the analysis of the allocation of personal disposable income to the different consumption goods and savings, an indirect-addilog-expenditure-system (IAES) has been constructed. Compared to the linear-expenditure-system (LES) the IAES to far more flexible and is not based upon the idea of minimum-consumption- or minimum-saving-quotas. On the other hand, marginal income shares are not fixed parameters. The IAES allows the derivation of a systematic savings- and consumption-function and supplies consistent income elasticities. But it will be shown that consistent demand systems are only restrictively able to consider all major determinants of the decision-problem consumption or saving. The derived system does not only neglect the effects of wealth on consumption and savings but also the results of real income fluctuations due to the business cycle. Also phenomena like unemployment and uncertainties regarding estimates of the future or inflation are neglected. With the help of an adjustment-procedure a part of these disadvantages has been eliminated. The adjustment with regard to the entire private consumption and savings supplied income elasticities which lead to an almost constant consumption- and savings-share in the period under investigation.     

Institutional Evolution through Purposeful Selection: The Constitutional Economics of John R. Commons

The paper relates John. R. Commons view on the roleof human design in institutional evolution to the views thathave been advanced on this matter by F. A. Hayek, in German ordo-liberalism,and in constitutional political economy. It is argued that Commonsconcept of purposeful selection points in the direction ofa theoretical perspective that consistently integrates the notionsof institutional evolution and constitutional design.     

Augmented serial rules for an excludable public good

Summary. We present a new class of rules named augmented serial rules for the provision of an excludable public good. First, we characterize this class by the four axioms of strategy-proofness, envy-freeness, access independence, and nonbossiness. Second, we identify two important subclasses by imposing an additional axiom: (i) anonymous augmented serial rules by anonymity, and (ii) Moulins serial rule by individual rationality.Received: 31 December 2002, Revised: 9 June 2004, JEL Classification Numbers: D71, D82, H41.This paper is a substantial revision of Serial cost sharing with simple games. I would like to thank Hervé Moulin, Yoshikatsu Tatamitani, an associate editor, and three anonymous referees for helpful suggestions and detailed comments. This research was partially supported by the Ministry of Education, Culture, Sports, Science, and Technology in Japan (Grant-in-Aid for 21st Century COE Program Microstructure and Mechanism Design in Financial Markets).     

On the Durability of King and Council: The Continuum Between Dictatorship and Democracy

In practice one rarely observes pure forms of dictatorship that lack a council, or pure forms of parliament that lack an executive. Generally government policies emerge from organizations that combine an executive branch of government, the king, with a cabinet or parliamentary branch, the council. This paper provides an explanation for this regularity, and also provides an evolutionary model of the emergence of democracy that does not require a revolution. The analysis demonstrates that the bipolar king and council constitutional template has a number of properties that gives it great practical efficiency as a method of information processing and as a very flexible institutional arrangement for making collective decisions.     

Convention, Social Order, and the Two Coordinations

The word coordination has two meanings, and thesemeanings are often conflated. One meaning, associated with ThomasSchelling, is seen in situations like choosing whether to driveon the left or the right; the drivers must coordinate to eachother's behavior. The other meaning, associated with FriedrichHayek, means that a concatenation of activities is arranged soas to produce good results. Along with the Schelling sense ofcoordination comes the notion of convention, such as drivingon the right. Some conventions are consciously designed; othersemerge without design (or are emergent). Along with the Hayeksense of coordination comes the notion of social order. Somesocial orders, such as the skeleton of activities within thefirm or within the hypothetical socialist economy, are consciouslyplanned. Other social orders, such as the catallaxy of the freesociety, function without central planning (or are spontaneous).Distinguishing between the two coordinations (and, in parallelfashion, between convention and social order) clarifies thinkingand resolves some confusions that have arisen in discussionsof coordination and spontaneous order. The key distinctionsare discussed in the context of the thought of, on the one hand,Menger, Schelling, David Lewis, and the recent path-dependencetheorists, and, on the other hand, Smith, Hayek, Polanyi, Coase,and the modern Austrian economists. The paper concludes witha typology that encompasses the several distinctions.