Public-good valuation and intra-family allocation

I derive values of marginal changes in a public good for two-person households, measured alternatively by household member i’s willingness to pay (WTP) for the good on behalf of the household, WTP _i (H), or by the sum of individual WTP values across family members, WTP(C). Households are assumed to allocate their resources in efficient Nash bargains over private and common household goods. WTP _i (H) is then defined by trade-offs between the public good and the household good, and WTP(C) by trade-offs of between the public good and private goods. WTP _i (H) is found to be higher (lower) than WTP(C) when member i has a relatively high (low) marginal valuation of the public good, but tends on average to equal WTP(C). As a consequence, individuals tend to represent households correctly on average when questioned about the household’s WTP for a public good, even when they are purely selfish and answer truthfully. Adding all members’ WTP answers on behalf of the household then leads to double counting. Pure and paternalistic altruism (the latter attached to consumption of the public good) move each member’s WTP on behalf of the household closer to the true sum of individual WTP, but only paternalistic altruism raises this sum.      

Learning from Others: A Welfare Analysis

This paper considers a smooth and noisy version of the statistical prediction model studied in the herding/informational cascades literature and compares market and optimal learning. The latter is characterized by defining a decentralized welfare benchmark as the solution to an infinite horizonteamproblem. Market behavior involves herding, in the sense that agents put too little weight on their private information for any given precision of public information, and yields underinvestment in the production of public information. However, both market and optimal learning involveslowlearning. Examples of the model include learning by doing, reaching consensus, and consumer learning about quality.Journal of Economic LiteratureClassification Numbers: D82, D83.     

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.     

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

Learning from private and public observations of othersʼ actions

We study the diffusion of dispersed private information in a large economy, where agents learn from the actions of others through two channels: a public channel, such as equilibrium market prices, and a private channel, for example local interactions. We show that, when agents learn only from the public channel, an initial release of public information increases agents? total knowledge at all times and increases welfare. When a private learning channel is present, this result is reversed: more initial public information reduces agents asymptotic knowledge by an amount in order of $\log (t)$ units of precision. When agents are sufficiently patient, this reduces welfare.     

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.     

The joint exploitation of a productive asset: a game-theoretic approach

Summary In the present paper we explore the set of equilibria in a game-theoretic model in which players can jointly exploit a productive asset. As in repeated games, we find that under certain circumstances there may be efficient as well as inefficient equilibria. In the model we study, efficient trigger-strategy equilibria may exist from some starting states (stocks of assets) but not others. More precisely, there is a stock level, sayy, such that an efficient trigger-strategy equilibrium exists from starting stocks greater than or equal toy, but not from those strictly less thany. (This statement is meant to include the cases in whichy is zero or infinite.) Under some circumstances, there may exist a new kind of equilibrium, which we call aswitching equilibrium. We show that, in our model, whenever y is positive (and finite), there is an open intervalI with upper endpoint y such that, from any starting stock inI there is an equilibrium of the dynamic game with the following structure: the players follow an inefficient but growing path until the stock reaches the levely, and then follow an (efficient) trigger strategy after that. The use of a continuous-time model enables us to conveniently decouple the delay of information from the time interval between decisions.We thank the C. V. Starr Center at New York University for research support. The views expressed here are those of the authors, and not necessarily those of AT&T Bell Laboratories.     

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.     

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.     

Stochastic models for capital growth

This paper relates to Wicksell's economic paradigm in presenting methods for determining the optimal cutting time of a single tree whose sizet periods into the future,X(t), is given by

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.     

Strategic market games with a finite horizon and incomplete markets

Summary. We study a strategic market game associated to an intertemporal economy with a finite horizon and incomplete markets. We demonstrate that generically, for any finite number of players, every sequentially strictly individually rational and default-free stream of allocations can be approximated by a full subgame-perfect equilibrium. As a consequence, imperfect competition may Pareto-dominate perfect competition when markets are incomplete. Moreover - and this contrasts with the main message conveyed by the market games literature - there exists a large open set of initial endowments for which full subgame-perfect equilibria do not converge to -efficient allocations when the number of players tends to infinity. Finally, strategic speculative bubbles may survive at full subgame-perfect equilibria.Received: 24 January 2002, Revised: 21 February 2003, JEL Classification Numbers: C72, D43, D52. Correspondence to: Gaël GiraudWe thank Tim Van Zandt for his comments.     

More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model

Summary. This paper studies monotone risk aversion, the aversion to monotone, mean-preserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by two functions, a utility function u in conjunction with a probability-perception function f. Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel and Lehmann [3,4] in Non-parametric Statistics. We present a characterization of the pairs (u,f) of monotone risk averse decision makers, based on an index of greediness G _u of the utility function u and an index of pessimism P _f of the probability perception function f: the decision maker is monotone risk averse if and only if . The index of greediness (non-concavity) of u is the supremum of taken over . The index of pessimism of f is the infimum of taken over 0 < v < 1. Thus, , with G _u = 1 iff u is concave. If then , i.e., f is majorized by the identity function. Since P _f = 1 for Expected Utility maximizers, forces u to be concave in this case; thus, the characterization of risk aversion as is a direct generalization from EU to RDEU. A novel element is that concavity of u is not necessary. In fact, u must be concave only if P _f = 1.Received: 10 April 2001, Revised: 18 November 2003, JEL Classification Numbers: D81. Correspondence to: Michéle CohenAlain Chateauneuf, Michéle Cohen, Isaac Meilijson: We are most grateful to Mark Machina, Peter Wakker and two anonymous referees for very helpful suggestions and comments.     

A model of the used car market with lemons and leasing

This article extends Kim's (1985 Kim, J-C. 1985. The market for lemons reconsidered: a model of the used car market with asymmetric information. American Economic Review, 75: 836–43.  [Google Scholar]) model of the used car market with asymmetric information to examine the possible impacts of leasing and Certified Pre-Owned (CPO) programs on the average quality of traded used cars in the market. The author assumed that a consumer can buy or lease a new car, or he/she can buy a used or a CPO car. While, like Kim (1985 Kim, J-C. 1985. The market for lemons reconsidered: a model of the used car market with asymmetric information. American Economic Review, 75: 836–43.  [Google Scholar]), the author assumed that the quality of a car depends on the maintenance level, the maintenance level in this model is chosen when a car is still a ‘new’ car, i.e. after the warranty ends. The model implied that the average quality of traded used cars can be either higher or lower than the average quality of nontraded used cars. The study also found that leasing and CPO have substantially improved the information mechanism between buyers and sellers of used cars, which, in turn, has helped reduce adverse selection and improved the average quality of traded used cars in the market.     

Speculative Attacks with Multiple Sources of Public Information*

We propose a speculative attack model in which agents receive multiple public signals. Diverse pieces of public information can be taken into account differently by different players and are likely to lead to different appreciations ex post. This process defines players' expected private values of a successful attack. The main result shows that equilibrium uniqueness depends on two conditions: (i) signals are sufficiently dispersed and (ii) private beliefs about signals' relative precision differ sufficiently. We derive some implications for information dissemination policy. Transparency in this context is multidimensional: it concerns the publicity of announcements, the number of signals disclosed and their precision.     

Information and efficiency in political stock markets: using computerized markets to predict election results

This study concentrates on four computerized political markets in Germany between 1990 and 1998. While this new method for the prediction of election events worked quite well in the USA it did not perform as well in Germany. Searching for the causes of this distinction it is shown that, in contrast to the findings of Forsythe et al. (1992 Forsythe, R, Nelson, F, Neumann, GR and Wright, J. 1992. Anatomy of an experimental political stock market. American Economic Review, 82: 1142–61.  ), (i) extraordinary profits were achieved less by people who took advantage of other people's anomalies than by those people who acquired an advantage from the existence of asymmetric information, (ii) the marginal trader hypothesis does not hold when applied to German markets, and that (iii) traders relied on public opinion polls. It is argued that these distinctions are caused by the differences in the German and the US voting systems. Additionally, it is shown that to a certain extent (iv) election markets were able to predict the contemporary mood of the electorate without the help of public opinion polls, (v) first of all the informed traders used public opinion polls as a source of information, and (vi) prices themselves became a source of information on which expectations were based.     

Giffen goods and market making

Summary. This paper shows that information effects per se are not responsible for the Giffen goods anomaly affecting traders demands in multi asset noisy, rational expectations equilibrium markets. The role that information plays in traders strategies also matters. In a market with risk averse, uninformed traders, informed agents have a dual trading motive: speculation and market making. The former entails using prices to assess the effect of error terms; the latter requires employing them to disentangle noise traders demands within aggregate orders. In a correlated environment this complicates the signal extraction problem and may generate upward sloping demand curves. Assuming (i) that competitive, risk neutral market makers price the assets or that (ii) uninformed traders risk tolerance coefficient grows unboundedly, removes the market making component from informed traders demands rendering them well behaved in prices.Received: 30 April 2002, Revised: 3 December 2003, JEL Classification Numbers: G100, G120, G140.Support from the Barcelona Economics Program of CREA and the Ente per gli Studi Monetari e Finanziari Luigi Einaudi, are gratefully acknowledged. I thank Anat Admati, Jordi Caballé, Giacinta Cestone, and Xavier Vives for useful suggestions. The comments provided by the Associate Editor and an anonymous referee greatly improved the papers exposition.     

The price of anarchy of serial, average and incremental cost sharing

We compute the price of anarchy (PoA) of three familiar demand games, i.e., the smallest ratio of the equilibrium to efficient surplus, over all convex preferences quasi-linear in money. For any convex cost, the PoA is at least in the average and serial games, where n is the number of users. It is zero in the incremental game for piecewise linear cost functions. With quadratic costs, the PoA of the serial game is , and for the average and incremental games. This generalizes if the marginal cost is convex or concave, and its elasticity is bounded.      

Collective choice functions on non-convex problems

Collective choice problems on sets in _boxclose_boxclose^n{\frak R}_+^n arise naturally in economics. Such problems have been extensively studied both in the theory of revealed preferences (Peters and Wakker, 1991) and in axiomatic bargaining theory under the assumption of convexity. However, our knowledge of collective choice functions on non-convex problems is still patchy. In this paper I study the existence and characterisation of continuous choice functions on the domain G\Gamma of comprehensive problems. The main result completely characterises rational choice functions that are continuous and satisfy Weak Pareto Optimality: they form the class of Monotone Path Choice Functions on G\Gamma. I also show that any discontinuous rational and weakly Pareto optimal choice function must be non- anonymous.     

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.